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Recent questions tagged permutationandcombination
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Number of Strings
Number of strings up to length $3$ on alphabet set $\sum$ = { a,b,c,d } are :(including,string of length zero)? $A) 16 $ $B) 85 $ $C) 128 $ $D) 64 $
asked
Oct 5, 2018
in
Combinatory
by
Lakshman Patel RJIT
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54.9k
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71
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discretemathematics
permutationandcombination
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0
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2
cormen 7th edition counting
How many ways are there for a horse race with three horses to finish if ties are possible?(Note: Two or three horses may tie) My answer is 9 but correct answer is 13. In the solution they have even considered the case of all three horses tying ... is it possible that in 3 horses race all three tie at third position? How can we get third without getting first and second?
asked
Oct 5, 2018
in
Combinatory
by
sushmita
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17.3k
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46
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permutationandcombination
discretemathematics
counting
+3
votes
1
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3
Combinatorics
There are n hats and k people (where k<n). $1)$ How many ways we can assign each person a hat? $2)$ How many ways we can assign each person atleast a hat?
asked
Oct 2, 2018
in
Combinatory
by
srestha
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117k
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131
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permutationandcombination
discretemathematics
+1
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1
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4
kenneth rosen
$1)$FIND THE COEFFICIENT OF $x^{10}$ from $(x^3+x^4+x^5+x^6+x^7....)^3$ $2)$FIND THE COEFFICIENT OF $x^9$ from $(1+x+x^2)^3$
asked
Oct 2, 2018
in
Combinatory
by
altamash
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445
points)

71
views
discretemathematics
permutationandcombination
+1
vote
0
answers
5
Generating permutation and combination
Is generating permutation and combination there in GATE CSE syllabus?
asked
Oct 1, 2018
in
GATE
by
aditi19
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5.1k
points)

31
views
permutationandcombination
+1
vote
2
answers
6
rosen
How many strings of six lowercase letters from the English alphabet contain a) the letter a? b) the letters a and b? c) the letters a and b in consecutive positions with a preceding b, with all the letters distinct? d) the letters a and b, where a is somewhere to the left of b in the string, with all the letters distinct?
asked
Sep 29, 2018
in
Combinatory
by
sushmita
Boss
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17.3k
points)

125
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discretemathematics
permutationandcombination
0
votes
0
answers
7
Combanotrics
Consider a set {1,2,3.....,10} a pair of distinct number is selected again & again, atleast how many of these pair have same sum?
asked
Sep 26, 2018
in
Combinatory
by
Raghav Khajuria
Junior
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763
points)

39
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permutationandcombination
0
votes
1
answer
8
Kenneth Rosen Edition 7th Exercise 8.4 Question 10 (Page No. 549 )
Find the coefficient of $x^9$ in the power series of each of these functions. a) $(x^3+x^5+x^6).(x^3+x^4).(x+x^2+x^3+x^4+⋯)$ b) $(1+x+x^2)^3$
asked
Sep 26, 2018
in
Combinatory
by
Na462
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6.9k
points)

166
views
generatingfunctions
discretemathematics
kennethrosen
permutationandcombination
0
votes
0
answers
9
Permutation and Combination
How many solutions are there to the equation : X1 + X2 + .... + X5 = 21 0 <= X1 <= 3 , 1 <= X2 < 4 , and X3 >= 15 ? Please solve it without using Generating function
asked
Sep 25, 2018
in
Mathematical Logic
by
Na462
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6.9k
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69
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permutationandcombination
0
votes
1
answer
10
RosenPigeonhole Principle
An arm wrestler is the champion for a period of 75 hours. (Here, by an hour, we mean a period starting from an exact hour, such as 1 P.M., until the next hour.) The arm wrestler had at least one match an hour, but no more than 125 total matches. Show that there is a period of consecutive hours during which the arm wrestler had exactly 24 matches.
asked
Sep 24, 2018
in
Combinatory
by
aditi19
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5.1k
points)

71
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pigeonholeprinciple
permutationandcombination
0
votes
1
answer
11
Combination
The number of ways can three 0’s, three 1’s and three 2’s be arranged, so that no three adjacent digits are the same in an arrangement is ________
asked
Sep 24, 2018
in
Combinatory
by
srestha
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117k
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50
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permutationandcombination
engineeringmathematics
discretemathematics
0
votes
0
answers
12
Kenneth Rosen Edition 6th Exercise 6.6 Question 5 (Page No. 457)
Find the number of primes less than 200 using the principle of inclusion–exclusion.
asked
Sep 22, 2018
in
Combinatory
by
sushmita
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17.3k
points)

218
views
kennethrosen
discretemathematics
permutationandcombination
inclusionexclusion
0
votes
0
answers
13
inclusion exclusion principle
In how many ways can we arrange the letters in the word '' ARRANGEMENT" such that 1.) there are exactly 2 consecutive same letters . 2.) atleast 3 consecutive same letters .
asked
Sep 22, 2018
in
Combinatory
by
sushmita
Boss
(
17.3k
points)

142
views
discretemathematics
permutationandcombination
probability
inclusionexclusion
0
votes
0
answers
14
ISI2016PCBCS8
Consider all possible trees with $n$ nodes. Let $k$ be the number of nodes with degree greater than 1 in a given tree. What is the maximum possible value of $k$? Justify your answer. Consider $2n$ committees, each having at least $2n$ persons, formed from a group of $4n$ persons. Prove that there exists at least one person who belongs to at least $n$ committees.
asked
Sep 18, 2018
in
Combinatory
by
jothee
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105k
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14
views
isi2016pcbcs
permutationandcombination
descriptive
0
votes
2
answers
15
Classroom
How many 5 letter (lower case) passwords are possible with with at least 2 'a's?
asked
Sep 18, 2018
in
Combinatory
by
Vikas Verma
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3.3k
points)

68
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permutationandcombination
+1
vote
2
answers
16
ISI2016PCBA3
A bit string is called legitimate if it contains no consecutive zeros $, e.g., 0101110$ is legitimate, where as $10100111$ is not. Let $a_n$ denote the number of legitimate bit strings of length $n$. Define $a_0=1$. Derive a recurrence relation for $a_n ( i.e.,$ express $a_n$ in terms of the preceding $a_i's).$
asked
Sep 18, 2018
in
Combinatory
by
jothee
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105k
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29
views
isi2016pcba
permutationandcombination
recurrencerelations
nongate
descriptive
0
votes
1
answer
17
Combination with repetition allowed
How many solutions are there to the inequality x1 + x2 + x3 ≤ 11 where x1, x2, x3 are nonnegative integers? Hint: introduce a variable x4 such that x1 + x2 + x3 + x4 = 11. Ans. C(4+111,11). My doubt is if the question had been x1 + x2 + x3 >= 11. then how would have we solved it ?
asked
Sep 18, 2018
in
Combinatory
by
Na462
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6.9k
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77
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permutationandcombination
engineeringmathematics
0
votes
0
answers
18
Permutation and Combination
How many ways are there to select 8 coins from a piggy bank with 100 pennies and 80 nickels ? Ans. C(2+81,8) Suppose the Question had been : How many ways are there to select 8 coins from a piggy bank with 6 pennies and 6 nickels? Now what would have been ... penny , 6 nickel 3 penny , 5 nickel and so on... But for a large number it would be a problem so how to do it ?
asked
Sep 18, 2018
in
Combinatory
by
Na462
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6.9k
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47
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permutationandcombination
0
votes
1
answer
19
#Combinatorics #Self Doubt
The number of ways of dividing 3 men and 3 women into 3 couples each consisting of a man and woman is: ____
asked
Sep 18, 2018
in
Combinatory
by
sakharam
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(
3k
points)

89
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permutationandcombination
0
votes
0
answers
20
Kenneth Rosen Edition 6th Exercise 5.5 Question 19 (Page No. 380)
Suppose that a large family has 14 children, including two sets of identical triplets, three sets of identical twins, and two individual children. How many ways are there to seat these children in a row of chairs if the ... they are neighborhood or not. But the question had asked for similar objects sit side by side. Please clarify
asked
Sep 17, 2018
in
Mathematical Logic
by
Abhijit Sen 4
(
399
points)

141
views
kennethrosen
discretemathematics
permutationandcombination
0
votes
1
answer
21
Kenneth Rosen Edition 7th Exercise 6.1 Question 45 (Page No. 397)
How many ways are there to seat six people around a circular table where two seating are considered the same when everyone has the same two neighbors without regard to whether they are right or left neighbors? what does ... the same when everyone has the same two neighbors without regard to whether they are right or left neighbors'?
asked
Sep 17, 2018
in
Combinatory
by
aditi19
Active
(
5.1k
points)

48
views
permutationandcombination
kennethrosen
discretemathematics
0
votes
0
answers
22
ISI2017MMA6
In a class of $80$ students, $40$ are girls and $40$ are boys. Also, exactly $50$ students wear glasses. Then the set of all possible numbers of boys without glasses is $\{0, \dots , 30\}$ $\{10, \dots , 30\}$ $\{0, \dots , 40\}$ none of these
asked
Sep 15, 2018
in
Combinatory
by
jothee
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(
105k
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46
views
isi2017mma
engineeringmathematics
discretemathematics
permutationandcombination
0
votes
1
answer
23
ISI2017MMA26
Let $n$ be the number of ways in which $5$ men and $7$ women can stand in a queue such that all the women stand consecutively. Let $m$ be the number of ways in which the same $12$ persons can stand in a queue such that exactly $6$ women stand consecutively. Then the value of $\frac{m}{n}$ is $5$ $7$ $\frac{5}{7}$ $\frac{7}{5}$
asked
Sep 15, 2018
in
Combinatory
by
jothee
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105k
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34
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isi2017mma
engineeringmathematics
discretemathematics
permutationandcombination
0
votes
0
answers
24
Kenneth Rosen Edition 6th Exercise 5.4 Theorem 4 (Page No. 368)
HI , someone please explain this theorem with an easy explanation
asked
Sep 15, 2018
in
Combinatory
by
Abhijit Sen 4
(
399
points)

31
views
permutationandcombination
kennethrosen
0
votes
1
answer
25
ISI2016MMA14
The number of terms independent of $x$ in the binomial expansion of $\bigg(3x^2 + \dfrac{1}{x}\bigg)^{10}$ is $0$ $1$ $2$ $5$
asked
Sep 13, 2018
in
Combinatory
by
jothee
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(
105k
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18
views
isi2016mma
permutationandcombination
binomialtheorem
+1
vote
0
answers
26
ISI2016MMA21
Let $A=\{1, 2, 3, 4, 5, 6, 7, 8 \}$. How many functions $f: A \rightarrow A$ can be defined such that $f(1)< f(2) < f(3)$? $\begin{pmatrix} 8 \\ 3 \end{pmatrix}$ $\begin{pmatrix} 8 \\ 3 \end{pmatrix} 5^8$ $\begin{pmatrix} 8 \\ 3 \end{pmatrix} 8^5$ $\frac{8!}{3!}$
asked
Sep 13, 2018
in
Calculus
by
jothee
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105k
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16
views
isi2016mmamma
functions
inequality
permutationandcombination
0
votes
0
answers
27
ISI2016MMA25
A integer is said to be a $\textbf{palindrome}$ if it reads the same forward or backward. For example, the integer $14541$ is a $5$digit palindrome and $12345$ is not a palindrome. How many $8$digit palindromes are prime? $0$ $1$ $11$ $19$
asked
Sep 13, 2018
in
Combinatory
by
jothee
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(
105k
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10
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isi2016mmamma
permutationandcombination
palindrome
0
votes
0
answers
28
ISI2016MMA30
A club with $n$ members is organized into four committees so that each member belongs to exactly two committees and each pair of committees has exactly one member in common. Then $n=4$ $n=6$ $n=8$ $n$ cannot be determined from the given information
asked
Sep 13, 2018
in
Combinatory
by
jothee
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(
105k
points)

13
views
isi2016mmamma
permutationandcombination
0
votes
0
answers
29
combinatrics
Number of ternary sequences possible with 6 ones ,6 twos and 4 zeros ,so that each 1 is followed by 2
asked
Sep 12, 2018
in
Combinatory
by
sajal singh
(
79
points)

60
views
permutationandcombination
0
votes
2
answers
30
Testbook Test Series: Combinatory  Permutations And Combinations
Number of ways of arranging the word "TESTBOOK" such that E always comes between O's.
asked
Sep 6, 2018
in
Combinatory
by
TUSHAR_BHATT
Active
(
1.3k
points)

85
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discretemathematics
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