Question

How many 8 letter words are there using the letters X, Y, Z containing at least one X and two Ys?

score 76 · Answer 1 · 2026-03-30 22:04:19

76

Views

How many 8 letter words are there using the letters X, Y, Z containing at least one X and two Ys?

Published on 30 Mar 2026 - 22:04

score 102 · Answer 2 · 2020-11-16 00:58:12

102

Views

How many injective functions $f$ are there from set $\{1, 2, . . . , n\}$ to the set $\{1, 2, . . . , n\}$ so that $f(x) = x$ for some $1 ≤ x ≤ n$?

Published on 16 Nov 2020 - 0:58

score 87 · Answer 3 · 2020-11-16 13:04:12

If $A$, $B$ and $C$ are subsets of a finite set $S$, how do we show how many elements of $S$ are contained in at least two of the subsets?

score 61 · Answer 4 · 2020-11-18 07:32:15

61

Views

Edge Coverings of Complete Graph With Loops

Published on 18 Nov 2020 - 7:32

score 203 · Answer 5 · 2026-04-01 07:44:49

203

Views

Reorganising alternating sum of products of binomial coefficients

Published on 01 Apr 2026 - 7:44

score 2.6k · Answer 6 · 2020-11-19 06:58:44

2.6k

Views

Determine the number of these subsets for which the sum of the three elements is a multiple of 3. [Read Full Q. Below]

Published on 19 Nov 2020 - 6:58

score 76 · Answer 7 · 2020-11-20 06:05:36

76

Views

Find the number of all ordered pair (a, b) such that a ∈ A, b ∈ B, a is not equal to b and a + b is even [Read Full Q. below]

Published on 20 Nov 2020 - 6:05

score 251 · Answer 8 · 2026-03-29 22:08:19

251

Views

Combinatorics problem - choosing $6$ cards out of $32$-card deck so that there are exactly three different suits (Inclusion-Exclusion)

Published on 29 Mar 2026 - 22:08

score 544 · Answer 9 · 2026-03-29 16:49:39

544

Views

10 ball as put in 7 boxes randomly. What is the probability that at least one box is empty?

Published on 29 Mar 2026 - 16:49

score 195 · Answer 10 · 2026-03-30 19:49:10

195

Views

How many words of length $10$ are there in which not all of the vowels A, E, I, O, U appear?

Published on 30 Mar 2026 - 19:49

score 203 · Answer 11 · 2020-11-22 17:13:25

203

Views

Prove $\sum_{k = 0}^{n}(-1)^{n - k} \binom{n}{k} \cdot k^n = n!$ and $\sum_{k = 0}^{n}(-1)^{n - k} \binom{n}{k} \cdot k^m = 0$

Published on 22 Nov 2020 - 17:13

score 57 · Answer 12 · 2026-03-29 22:07:34

57

Views

$9$-card-long (or longer) straight flush in a $13$-card hand

Published on 29 Mar 2026 - 22:07

score 64 · Answer 13 · 2026-03-26 07:46:54

64

Views

A special kind of sieve. Find lower bound for cardinality of a given set.

Published on 26 Mar 2026 - 7:46

score 627 · Answer 14 · 2020-11-27 06:55:35

627

Views

count of matrix of 0,1 in which each row and each column have at least one 1.

Published on 27 Nov 2020 - 6:55

score 634 · Answer 15 · 2020-11-27 10:46:47

634

Views

Possible arrangements of the word ARRANGEMENT

Published on 27 Nov 2020 - 10:46

List Question

How many 8 letter words are there using the letters X, Y, Z containing at least one X and two Ys?

How many injective functions $f$ are there from set $\{1, 2, . . . , n\}$ to the set $\{1, 2, . . . , n\}$ so that $f(x) = x$ for some $1 ≤ x ≤ n$?

If $A$, $B$ and $C$ are subsets of a finite set $S$, how do we show how many elements of $S$ are contained in at least two of the subsets?

Edge Coverings of Complete Graph With Loops

Reorganising alternating sum of products of binomial coefficients

Determine the number of these subsets for which the sum of the three elements is a multiple of 3. [Read Full Q. Below]

Find the number of all ordered pair (a, b) such that a ∈ A, b ∈ B, a is not equal to b and a + b is even [Read Full Q. below]

Combinatorics problem - choosing $6$ cards out of $32$-card deck so that there are exactly three different suits (Inclusion-Exclusion)

10 ball as put in 7 boxes randomly. What is the probability that at least one box is empty?

How many words of length $10$ are there in which not all of the vowels A, E, I, O, U appear?

Prove $\sum_{k = 0}^{n}(-1)^{n - k} \binom{n}{k} \cdot k^n = n!$ and $\sum_{k = 0}^{n}(-1)^{n - k} \binom{n}{k} \cdot k^m = 0$

$9$-card-long (or longer) straight flush in a $13$-card hand

A special kind of sieve. Find lower bound for cardinality of a given set.

count of matrix of 0,1 in which each row and each column have at least one 1.

Possible arrangements of the word ARRANGEMENT

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