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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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3 days
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Combinatory
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Abhinavg
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pegionhole
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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
answered
4 days
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Combinatory
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Soumya29
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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 at-least 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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permutations-and-combinations
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
ago
in
Combinatory
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Mk Utkarsh
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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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testbook-test-series
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0
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0
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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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599
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42
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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?
asked
Apr 12
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Combinatory
by
Jason
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1
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8
Kenneth Rosen, Generating Functions, Exercise - 6.4 QNO-33
answered
Apr 12
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Combinatory
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pankaj_vir
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93
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kenneth-rosen
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+3
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1
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9
Test Series
answered
Apr 12
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Combinatory
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ankitgupta.1729
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permutations-and-combinations
factorial
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10
Indistinguishable objects and Indistinguishable boxes
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Apr 7
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Combinatory
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Soumya29
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58
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permutations-and-combinations
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1
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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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permutations-and-combinations
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
in
Combinatory
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yash789
(
27
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293
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permutations-and-combinations
isi2004
discrete-mathematics
normal
+1
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2
answers
13
Kenneth Rosen (Special Indian Edition) Section 6.1 Exercise Problem #9d
answered
Apr 4
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Combinatory
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pankaj_vir
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recurrence-relation
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2
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14
Kenneth Rosen , Recurrence relation, Exercise 6.1 Qno. - 19
answered
Apr 2
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Combinatory
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pankaj_vir
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51
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+10
votes
5
answers
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
by
Hitesh
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289
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501
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permutations-and-combinations
isi2004
0
votes
1
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16
Kenneth Rosen Recurrence Relation Example 8
answered
Apr 1
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Combinatory
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abhishekmehta4u
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84
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kenneth-rosen
recurrence
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2
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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
in
Combinatory
by
pankaj_vir
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6.3k
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96
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generating-functions
discrete-mathematics
+25
votes
7
answers
18
GATE 2016-1-27
Consider the recurrence relation $a_1 =8 ,a_n =6n^2 +2n+a_{n-1}.$ Let $a_{99}=K\times 10^4$. The value of $K$ is __________.
answered
Mar 31
in
Combinatory
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pankaj_vir
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4.8k
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gate2016-1
permutations-and-combinations
recurrence
normal
numerical-answers
+24
votes
5
answers
19
GATE2015-1_26
$\sum\limits_{x=1}^{99}\frac{1}{x(x+1)}$ = __________________.
answered
Mar 31
in
Combinatory
by
pankaj_vir
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6.3k
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1.4k
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gate2015-1
permutations-and-combinations
normal
numerical-answers
summation
+3
votes
2
answers
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
in
Combinatory
by
ankitgupta.1729
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4.2k
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88
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permutations-and-combinations
discrete-mathematics
+24
votes
8
answers
21
GATE2014-1-49
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 4-pennant. The set of all possible 1-pennants is ${(1)}$, the set of all possible 2-pennants 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 10-pennants is________
answered
Mar 24
in
Combinatory
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Prateek K
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1.2k
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1.7k
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gate2014-1
permutations-and-combinations
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+1
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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
by
Sukanya Das
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11.2k
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113
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discrete-mathematics
kenneth-rosen
counting
permutations-and-combinations
+4
votes
1
answer
23
Discrete Mathematics By Kenneth H Rosen Counting
answered
Mar 20
in
Combinatory
by
Sukanya Das
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78
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discrete-mathematics
permutations-and-combinations
counting
+4
votes
2
answers
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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engineering-mathematics
permutations-and-combinations
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
by
Shivam14chd
(
107
points)
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116
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permutations-and-combinations
+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)
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106
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permutations-and-combinations
engineering-mathematics
0
votes
0
answers
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
by
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
by
Ananya Jaiswal 1
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1.2k
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59
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probability
random-variable
0
votes
1
answer
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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kenneth-rosen
discrete-mathematics
counting
0
votes
0
answers
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
points)
|
27
views
discrete-mathematics
functions
relations
set-theory&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
Boss
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11.7k
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79
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permutations-and-combinations
+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
in
Combinatory
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monanshi
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301
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+1
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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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kenneth-rosen
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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
in
Combinatory
by
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
in
Combinatory
by
Sukanya Das
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11.2k
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119
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discrete
discrete-mathematics
kenneth-rosen
counting
0
votes
3
answers
37
Self doubt generating function
Equation: $x+y=10$ and we are asked to find out the number of a non-negative integral solution of this equation.
answered
Feb 25
in
Combinatory
by
gari
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142
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generating-functions
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1
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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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222
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discrete-mathematics
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+15
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4
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39
TIFR2010-A-12
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
in
Combinatory
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Lakshman Patel RJIT
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520
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tifr2010
generating-functions
+2
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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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