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Recent questions and answers in Combinatory
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#Pigeonhole Principle Doubt
How many positive integers not exceeding 1000 are divisible by 7? So, the doubt here is why we are taking floor function while calculating this .
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Combinatory
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Abhinavg
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pegionhole
#counting
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2
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2
GATE question
Q. 6 Xs has to be placed in the figure below such that each row contains at least one X. In how many ways can this be done? a) 160 b) 180 c) 170 d) 26
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Combinatory
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Soumya29
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permutationsandcombinations
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Combinations with 3 Jugs
You are given 3 jugs A,B and C of capacities 8, 5 and 3 liters, respectively. A is filled and B and C are empty. Total amount of water is 8 liters. How many different combinations are possible with at least one of the jug being empty or atleast one of them being full. For example $(8,0,0)$ , $(4,4,0)$ , $(5,3,0)$
[closed]
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5 days
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Combinatory
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Mk Utkarsh
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52
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permutationsandcombinations
0
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1
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4
Combinatorics
How many ways we can move from a point (a,b) to a point (i,j) in a coordinate system. Here i>a and j>b and at each step you can move to the right or in the upward direction.
answered
6 days
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Combinatory
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Mk Utkarsh
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permutationsandcombinations
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1
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5
COMBINATRICS
NUMBER OF WAYS WE CAN ARRAYS LETTERS OF THE WORD "TESTBOOK" SO THAT NO TWO VOWELS ARE TOGETHER IS
answered
Apr 13
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Combinatory
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Subarna Das
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testbooktestseries
permutationsandcombinations
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6
COMBINATRICS
NUMBER OF WAYS IN WHICH CORNER OF THE SQUARE CAN BE COLORED WITH TWO COLORS. (ITS IS PERMISSIBLE TO USE A SINGLE COLOUR ON ALL FOUR CORNER)
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Apr 13
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Combinatory
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Ismail
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7
Permutation of 4 Gs out of 5 Gs
Given symbols: $GGGGGAAATTTECCS$ No of ways such that exactly 4 Gs out of 5 Gs are together. I am getting$ \frac{11! × 11}{3!×3!×2!} $. Some one verify it?
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Apr 12
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Combinatory
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Jason
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94
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1
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8
Kenneth Rosen, Generating Functions, Exercise  6.4 QNO33
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Apr 12
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Combinatory
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pankaj_vir
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93
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kennethrosen
discretemathematics
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1
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9
Test Series
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Apr 12
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10
Indistinguishable objects and Indistinguishable boxes
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Apr 7
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11
Permutations
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Apr 6
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Combinatory
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Tesla!
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isisamplepapers
+6
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3
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12
ISI 2004 MIII
The number of permutation of {1,2,3,4,5} that keep at least one integer fixed is. 81 76 120 60
answered
Apr 6
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Combinatory
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yash789
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27
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293
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permutationsandcombinations
isi2004
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2
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13
Kenneth Rosen (Special Indian Edition) Section 6.1 Exercise Problem #9d
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Apr 4
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pankaj_vir
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14
Kenneth Rosen , Recurrence relation, Exercise 6.1 Qno.  19
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Apr 2
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Combinatory
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pankaj_vir
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5
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15
ISI 2004 MIII
In how many ways can three person, each throwing a single die once, make a score of 11 22 27 24 38
answered
Apr 1
in
Combinatory
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Hitesh
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289
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501
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permutationsandcombinations
isi2004
0
votes
1
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16
Kenneth Rosen Recurrence Relation Example 8
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Apr 1
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Combinatory
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abhishekmehta4u
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kennethrosen
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17
Generating functions
What will be the coefficient of x^17 in the expansion of (x+x^2+x^3+x^4+x^5+x^6)^4?
answered
Mar 31
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Combinatory
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pankaj_vir
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generatingfunctions
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+25
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7
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18
GATE 2016127
Consider the recurrence relation $a_1 =8 ,a_n =6n^2 +2n+a_{n1}.$ Let $a_{99}=K\times 10^4$. The value of $K$ is __________.
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Mar 31
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Combinatory
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pankaj_vir
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gate20161
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5
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19
GATE20151_26
$\sum\limits_{x=1}^{99}\frac{1}{x(x+1)}$ = __________________.
answered
Mar 31
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Combinatory
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pankaj_vir
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1.4k
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gate20151
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20
Combinatorics
Sanjay have 9 distinct paths (1,2,3.....,9) from his home to his work place. He works from Monday to Friday every week, he does not go to work on Saturdays and Sundays. Every Sunday he schedules that which path he will take for each ... The only restriction is that he cannot select even number paths on 2 consecutive days. How many possible combinations he have to make his schedule?
answered
Mar 26
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Combinatory
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ankitgupta.1729
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8
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21
GATE2014149
A pennant is a sequence of numbers, each number being 1 or 2. An $n$pennant is a sequence of numbers with sum equal to $n$. For example, $(1,1,2)$ is a 4pennant. The set of all possible 1pennants is ${(1)}$, the set of all possible 2pennants is ${(2), (1,1 ... ,1,1), (1,2)}$. Note that the pennant $(1,2)$ is not the same as the pennant $(2,1)$. The number of 10pennants is________
answered
Mar 24
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Combinatory
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Prateek K
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gate20141
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2
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22
Counting Kenneth Rosen Exercise
How many strings with seven or more characters can be formed from the letters of the word $\text{EVERGREEN}$ ?
answered
Mar 22
in
Combinatory
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Sukanya Das
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113
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discretemathematics
kennethrosen
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permutationsandcombinations
+4
votes
1
answer
23
Discrete Mathematics By Kenneth H Rosen Counting
answered
Mar 20
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Combinatory
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Sukanya Das
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78
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discretemathematics
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counting
+4
votes
2
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24
Combination (Repetition)
A girl has to choose 4 items from a bucket which contains 3 red, 3 green, and 4 blue balls, now in how many ways she can do this?
answered
Mar 19
in
Combinatory
by
akshat sharma
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1.5k
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103
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engineeringmathematics
permutationsandcombinations
0
votes
0
answers
25
self doubt
Three men have 4 coats, 5 waist coats, and 6 caps. In how many ways can they wear them? Three men have 4 coats, 5 waist coats, and 6 caps. In how many ways can they wear any type of them?
asked
Mar 18
in
Combinatory
by
Kaluti
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5.3k
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34
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+1
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5
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26
Combinatorics
Three ladies have each brought a child for admission to a school. The head of the school wishes to interview the six people one by one, taking care that no child is interviewed before its mother. In how many different ways can the interviews be arranged? $6$ $36$ $72$ $90$
answered
Mar 18
in
Combinatory
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Shivam14chd
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107
points)

116
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permutationsandcombinations
+3
votes
2
answers
27
Permutation and combination
in how many ways 2 alike apple, 3 alike orange and 4 alike mango can be given to 3 children if each child can have none or 1 or more than 1 fruits.
answered
Mar 17
in
Combinatory
by
Shivam14chd
(
107
points)

106
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permutationsandcombinations
engineeringmathematics
0
votes
0
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28
Number of unique solution
Suppose there is an equation $x_{1}+x_{2}+...........x_{r}=n$ Then number of unique solution in this given equation?
asked
Mar 13
in
Combinatory
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srestha
Veteran
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81.7k
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60
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counting
0
votes
0
answers
29
sheldon ross
Three balls are to be randomly selected without replacement from an urn containing $20$ balls numbered $1$ through $20$. If we bet that at least one of the balls that are drawn has a number as large as or larger than $17$, what is the probability that we win the bet?
asked
Mar 10
in
Combinatory
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Ananya Jaiswal 1
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probability
randomvariable
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votes
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30
Rosen Example no.  9
Suppose that a computer science laboratory has $15$ workstations and $10$ servers. A cable can be used to directly connect a workstation to a server. For each server, only one direct connection to that server can be active at any time. We ... minimum number of direct connections needed to achieve this goal? Please Explain in this question how pigeonhole principle is applied .
answered
Mar 6
in
Combinatory
by
Deepakk Poonia (Dee)
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2.8k
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43
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kennethrosen
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counting
0
votes
0
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31
Composition of function
"f:A>B & g:C>D are 2 functions then for their composition B should be equal to C." But if B is not equal to C then composition is possible or not? Eg:A={1,2,} B={3,4} C={4,5} D={6,7} then can fog be computed Or not? f={(1,3), (2,4)} g={(4,6),(5,7)} gof={(2,6)} is it true or not? I hope my question could be understood:)
[closed]
asked
Mar 3
in
Combinatory
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MayankSharma
(
121
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27
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discretemathematics
functions
relations
settheory&algebra
0
votes
0
answers
32
Combinatorics
There are total 21 identical balls in a shop and 7 children. In how many ways can 7 children claim the balls? (it is not necessary to claim all the balls)
asked
Mar 3
in
Combinatory
by
Mk Utkarsh
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11.7k
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79
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permutationsandcombinations
+2
votes
2
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33
rosen exercise problem
How many bit strings of length 10 contain at least three 1s and at least three 0s? My Approach:> using product rule There are 3 subtask following (filling 3 ones in 10 places) = (filling 3 zeros in remaing 7 places) = (filling remaining 4 places) = ... ** which is greater than (total number of string). Now , i want to know what is wrong in my apporach. please explain..
answered
Mar 3
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Combinatory
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monanshi
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9.4k
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301
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discretemathematics
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1
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34
Kenneth Rosen Ex.10 counting
How many ways are there to put four different employees into three indistinguishable offices when each office can contain any number of employees?
answered
Mar 2
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Combinatory
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Sukanya Das
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11.2k
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88
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kennethrosen
discretemathematics
counting
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+2
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2
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35
Permutation and Combination
A train has 12 stations on it's route and it has to stopped at any 4 station, such that no two stations are consecutive. find number of possible way for choosing 4 station's?
answered
Mar 1
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Combinatory
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Mk Utkarsh
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+3
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1
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36
Combination Ex.14 Kenneth Rosen
How many bit strings of length $n$ contain exactly $r$ $1's$?
answered
Mar 1
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Combinatory
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Sukanya Das
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11.2k
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119
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discrete
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0
votes
3
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37
Self doubt generating function
Equation: $x+y=10$ and we are asked to find out the number of a nonnegative integral solution of this equation.
answered
Feb 25
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Combinatory
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gari
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3.2k
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generatingfunctions
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38
Generating function doubt
Please give me clarification
answered
Feb 24
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Combinatory
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Sukannya
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discretemathematics
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4
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39
TIFR2010A12
The coefficient of $x^{3}$ in the expansion of $(1 + x)^{3} (2 + x^{2})^{10}$ is. $2^{14}$ $31$ $\left ( \frac{3}{3} \right ) + \left ( \frac{10}{1} \right )$ $\left ( \frac{3}{3} \right ) + 2\left ( \frac{10}{1} \right )$ $\left ( \frac{3}{3} \right ) \left ( \frac{10}{1} \right ) 2^{9}$
answered
Feb 24
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Combinatory
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Lakshman Patel RJIT
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520
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tifr2010
generatingfunctions
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0
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40
Extended Binomial Coefficients
Find the value of extended Binomial Coefficient $\binom{1/2}{3}$
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Feb 24
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Combinatory
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Mk Utkarsh
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67
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