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Recent questions tagged permutationandcombination
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The Interesting combination sum problems
Find the number of possible solutions for $x,y,z$ for each the following cases. $Case\ 1.$ Case of unlimited repetition. $x + y +z = 10$ and $x \geq 0\ , y \geq 0,\ z \geq 0 $ $Case\ 2 $ Case of unlimited repetition with variable lower bounds $x + y +z = 10$ and ... variable. $x + y +z = 10$ and $8 \geq x \geq 1\ , \ 20 \geq y \geq 2 \ , 12 \geq z \geq 3\ $
asked
Nov 1
in
Combinatory
by
Satbir
Boss
(
20.6k
points)

112
views
permutationandcombination
+1
vote
2
answers
2
ISI2014DCG1
Let $(1+x)^n = C_0+C_1x+C_2x^2+ \dots + C_nx^n$, $n$ being a positive integer. The value of $\bigg( 1+\dfrac{C_0}{C_1} \bigg) \bigg( 1+\dfrac{C_1}{C_2} \bigg) \cdots \bigg( 1+\dfrac{C_{n1}}{C_n} \bigg)$ is $\bigg( \frac{n+1}{n+2} \bigg) ^n$ $ \frac{n^n}{n!} $ $\bigg( \frac{n}{n+1} \bigg) ^n$ $ \frac{(n+1)^n}{n!} $
asked
Sep 23
in
Combinatory
by
Arjun
Veteran
(
422k
points)

117
views
isi2014dcg
permutationandcombination
binomialtheorem
+1
vote
2
answers
3
ISI2014DCG18
$^nC_0+2^nC_1+3^nC_2+\cdots+(n+1)^nC_n$ equals $2^n+n2^{n1}$ $2^nn2^{n1}$ $2^n$ none of these
asked
Sep 23
in
Combinatory
by
Arjun
Veteran
(
422k
points)

26
views
isi2014dcg
permutationandcombination
binomialtheorem
+1
vote
0
answers
4
ISI2014DCG32
Consider $30$ multiplechoice questions, each with four options of which exactly one is correct. Then the number of ways one can get only the alternate questions correctly answered is $3^{15}$ $2^{31}$ $2 \times \begin{pmatrix} 30 \\ 15 \end{pmatrix}$ $2 \times 3^{15}$
asked
Sep 23
in
Combinatory
by
Arjun
Veteran
(
422k
points)

36
views
isi2014dcg
permutationandcombination
+1
vote
1
answer
5
ISI2014DCG34
The following sum of $n+1$ terms $2 + 3 \times \begin{pmatrix} n \\ 1 \end{pmatrix} + 5 \times \begin{pmatrix} n \\ 2 \end{pmatrix} + 9 \times \begin{pmatrix} n \\ 3 \end{pmatrix} + 17 \times \begin{pmatrix} n \\ 4 \end{pmatrix} + \cdots$ up to $n+1$ terms is equal to $3^{n+1}+2^{n+1}$ $3^n \times 2^n$ $3^n + 2^n$ $2 \times 3^n$
asked
Sep 23
in
Combinatory
by
Arjun
Veteran
(
422k
points)

23
views
isi2014dcg
permutationandcombination
binomialtheorem
summation
+1
vote
1
answer
6
ISI2014DCG41
The number of permutations of the letters $a, b, c$ and $d$ such that $b$ does not follow $a,c$ does not follow $b$, and $c$ does not follow $d$, is $11$ $12$ $13$ $14$
asked
Sep 23
in
Combinatory
by
Arjun
Veteran
(
422k
points)

26
views
isi2014dcg
permutationandcombination
+1
vote
1
answer
7
ISI2014DCG63
If $^nC_{r1}=36$, $^nC_r=84$ an $^nC_{r+1}=126$ then $r$ is equal to $1$ $2$ $3$ none of these
asked
Sep 23
in
Combinatory
by
Arjun
Veteran
(
422k
points)

12
views
isi2014dcg
permutationandcombination
0
votes
1
answer
8
ISI2014DCG66
Consider all possible words obtained by arranging all the letters of the word $\textbf{AGAIN}$. These words are now arranged in the alphabetical order, as in a dictionary. The fiftieth word in this arrangement is $\text{IAANG}$ $\text{NAAGI}$ $\text{NAAIG}$ $\text{IAAGN}$
asked
Sep 23
in
Combinatory
by
Arjun
Veteran
(
422k
points)

12
views
isi2014dcg
permutationandcombination
arrangingletters
+1
vote
1
answer
9
ISI2014DCG71
Five letters $A, B, C, D$ and $E$ are arranged so that $A$ and $C$ are always adjacent to each other and $B$ and $E$ are never adjacent to each other. The total number of such arrangements is $24$ $16$ $12$ $32$
asked
Sep 23
in
Combinatory
by
Arjun
Veteran
(
422k
points)

20
views
isi2014dcg
permutationandcombination
arrangements
circularpermutation
0
votes
1
answer
10
ISI2014DCG72
The sum $\sum_{k=1}^n (1)^k \:\: {}^nC_k \sum_{j=0}^k (1)^j \: \: {}^kC_j$ is equal to $1$ $0$ $1$ $2^n$
asked
Sep 23
in
Combinatory
by
Arjun
Veteran
(
422k
points)

26
views
isi2014dcg
permutationandcombination
summation
0
votes
1
answer
11
ISI2015DCG21
The value of the term independent of $x$ in the expansion of $(1x)^2(x+\frac{1}{x})^7$ is $70$ $70$ $35$ None of these
asked
Sep 18
in
Combinatory
by
gatecse
Boss
(
16.6k
points)

10
views
isi2015dcg
permutationandcombination
binomialtheorem
+1
vote
1
answer
12
ISI2015DCG24
If the letters of the word $\textbf{COMPUTER}$ be arranged in random order, the number of arrangements in which the three vowels $O, U$ and $E$ occur together is $8!$ $6!$ $3!6!$ None of these
asked
Sep 18
in
Combinatory
by
gatecse
Boss
(
16.6k
points)

12
views
isi2015dcg
permutationandcombination
arrangements
+1
vote
1
answer
13
CMI2019A4
There are five buckets, each of which can be open or closed. An arrangement is a specification of which buckets are open and which bucket are closed. Every person likes some of the arrangements and dislikes the rest. You host a party, and amazingly, no two people on the guest list have the ... What is the maximum number of guests possible? $5^{2}$ $\binom{5}{2}$ $2^{5}$ $2^{2^{5}}$
asked
Sep 13
in
Combinatory
by
gatecse
Boss
(
16.6k
points)

30
views
cmi2019
permutationandcombination
arrangements
0
votes
1
answer
14
CMI2019A5
Let $\pi=[x_{1},x_{2},\cdots,x_{n}]$ be a permutation of $\{1,2,\cdots,n\}.$ For $k<n,$ we say that $\pi$ has its first ascent at $k$ if $x_{1}>x_{2}\cdots>x_{k}$ and $x_{k}<x_{k+1}.$ How many permutations have their first ascent at $k?$ $\binom{n}{k}\binom{n}{(k+1)}$ $\frac{n!}{k!}\frac{n!}{(k+1)!}$ $\frac{n!}{(k+1)!}\frac{n!}{(k+2)!}$ $\binom{n}{(k+1)}\binom{n}{(k+2)}$
asked
Sep 13
in
Others
by
gatecse
Boss
(
16.6k
points)

33
views
cmi2019
permutationandcombination
+1
vote
1
answer
15
CMI2018A5
How many paths are there in the plane from $(0,0)$ to $(m,n)\in \mathbb{N}\times \mathbb{N},$ if the possible steps from $(i,j)$ are either $(i+1,j)$ or $(i,j+1)?$ $\binom{2m}{n}$ $\binom{m}{n}$ $\binom{m+n}{n}$ $m^{n}$
asked
Sep 13
in
Combinatory
by
gatecse
Boss
(
16.6k
points)

32
views
cmi2018
permutationandcombination
paths
+3
votes
1
answer
16
ISI MTECH CS 2019 INTERVIEW question
As due to rain, the match between the teams in ICC world cup got canceled , So lets the total team be 10, exclude semi finals and finals , consider only league match, What is the total number of matches that played between the teams ... many ways those n matches can be conducted ? Source : https://gateoverflow.in/blog/8548/isimtechcs2019interviewexperience
asked
Aug 8
in
Combinatory
by
Shaik Masthan
Veteran
(
64k
points)

138
views
permutationandcombination
+2
votes
2
answers
17
UGCNETJune2019II2
How many ways are there to place $8$ indistinguishable balls into four distinguishable bins? $70$ $165$ $^8C_4$ $^8P_4$
asked
Jul 2
in
Combinatory
by
Arjun
Veteran
(
422k
points)

350
views
ugcnetjune2019ii
permutationandcombination
+1
vote
2
answers
18
UGCNETJune2019II3
How many bit strings of length ten either start with a $1$ bit or end with two bits $00$ ? $320$ $480$ $640$ $768$
asked
Jul 2
in
Combinatory
by
Arjun
Veteran
(
422k
points)

249
views
ugcnetjune2019ii
permutationandcombination
inclusionexclusion
+1
vote
1
answer
19
UGCNETJune2019II7
How many cards must be selected from a standard deck of $52$ cards to guarantee that at least three hearts are present among them? $9$ $13$ $17$ $42$
asked
Jul 2
in
Combinatory
by
Arjun
Veteran
(
422k
points)

202
views
ugcnetjune2019ii
permutationandcombination
pigeonholeprinciple
0
votes
1
answer
20
Sheldon Ross Example5n
Compute the probability that if 10 married couples are seated at random at a round table, then no wife sits next to her husband 1 wife sits next to her husband. pick one of the 10 couples=$\binom{10}{1}$. These couples can interchange their position such that ... sits together=$\frac{N}{19!}$ so probability that no couple sits together=$1\frac{N}{19!}$ is this correct?
asked
Jun 11
in
Probability
by
aditi19
Active
(
5k
points)

169
views
permutationandcombination
probability
discretemathematics
sheldonross
+1
vote
1
answer
21
#ACE ACADEMY BOOKLET QUESTION
The solution of $\sqrt{a_n} – 2\sqrt{a_{n1}} + \sqrt{a_{n2}} = 0$ where $a_0 = 1$ and $a_1 = 2$ is ${\Big[\frac{2^{n+1} + (1)^n}{3}\Big]}^2$ $(n+1)^2$ $(n1)^3$ $(n1)^2$
asked
Jun 5
in
Combinatory
by
`JEET
Boss
(
11.2k
points)

120
views
discretemathematics
permutationandcombination
recurrence
#recurrencerelations
0
votes
3
answers
22
Self DoubtCombinatory
In how many ways we can put $n$ distinct balls in $k$ dintinct bins?? Will it be $n^{k}$ or $k^{n}$?? Taking example will be easy way to remove this doubt or some other ways possible??
asked
May 25
in
Combinatory
by
srestha
Veteran
(
116k
points)

101
views
discretemathematics
permutationandcombination
+1
vote
2
answers
23
Permutation & Combination Self Doubt
How many 4 letter combinations can be made with the help of letters of the word STATISTICS?
asked
May 16
in
Numerical Ability
by
Pooja Khatri
Boss
(
10.8k
points)

142
views
permutationandcombination
generalaptitude
+1
vote
1
answer
24
ISI2018MMA10
A new flag of ISI club is to be designed with $5$ vertical strips using some or all of the four colors: green, maroon, red and yellow. In how many ways this can be done so that no two adjacent strips have the same color? $120$ $324$ $424$ $576$
asked
May 11
in
Combinatory
by
akash.dinkar12
Boss
(
41.7k
points)

50
views
isi2018mma
engineeringmathematics
discretemathematics
permutationandcombination
+1
vote
2
answers
25
ISI2019MMA27
A general election is to be scheduled on $5$ days in May such that it is not scheduled on two consecutive days. In how many ways can the $5$ days be chosen to hold the election? $\begin{pmatrix} 26 \\ 5 \end{pmatrix}$ $\begin{pmatrix} 27 \\ 5 \end{pmatrix}$ $\begin{pmatrix} 30 \\ 5 \end{pmatrix}$ $\begin{pmatrix} 31 \\ 5 \end{pmatrix}$
asked
May 7
in
Combinatory
by
Sayan Bose
Loyal
(
7.1k
points)

2.8k
views
isi2019mma
engineeringmathematics
discretemathematics
permutationandcombination
0
votes
2
answers
26
ISI2019MMA20
Suppose that the number plate of a vehicle contains two vowels followed by four digits. However, to avoid confusion, the letter $‘O’$ and the digit $‘0’$ are not used in the same number plate. How many such number plates can be formed? $164025$ $190951$ $194976$ $219049$
asked
May 7
in
Combinatory
by
Sayan Bose
Loyal
(
7.1k
points)

358
views
isi2019mma
engineeringmathematics
discretemathematics
permutationandcombination
0
votes
1
answer
27
ISI2019MMA4
Suppose that $6$digit numbers are formed using each of the digits $1, 2, 3, 7, 8, 9$ exactly once. The number of such $6$digit numbers that are divisible by $6$ but not divisible by $9$ is equal to $120$ $180$ $240$ $360$
asked
May 6
in
Combinatory
by
Sayan Bose
Loyal
(
7.1k
points)

210
views
isi2019mma
engineeringmathematics
discretemathematics
permutationandcombination
0
votes
1
answer
28
ISI2019MMA2
The number of $6$ digit positive integers whose sum of the digits is at least $52$ is $21$ $22$ $27$ $28$
asked
May 6
in
Combinatory
by
Sayan Bose
Loyal
(
7.1k
points)

254
views
isi2019mma
engineeringmathematics
discretemathematics
permutationandcombination
0
votes
1
answer
29
Rosen 7e Recurrence Relation Exercise8.1 Question no25 page no511
How many bit sequences of length seven contain an even number of 0s? I'm trying to solve this using recurrence relation Is my approach correct? Let T(n) be the string having even number of 0s T(1)=1 {1} T(2)=2 {00, 11} T(3)=4 {001, ... add 0 to strings of length n1 having odd number of 0s T(n)=T(n1) Hence, we have T(n)=2T(n1)
asked
Apr 29
in
Combinatory
by
aditi19
Active
(
5k
points)

62
views
kennethrosen
discretemathematics
permutationandcombination
#recurrencerelations
recurrence
0
votes
2
answers
30
Rosen 7e Exercise8.1 Question no10 Page no511
Find a recurrence relation for the number of bit strings of length n that contain the string 01.
asked
Apr 28
in
Combinatory
by
aditi19
Active
(
5k
points)

54
views
kennethrosen
discretemathematics
permutationandcombination
#recurrencerelations
recurrence
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