Question

Proving $\sum_{k=1}^{n} k \binom{n}{k} = n \cdot 2^{n-1}$ by double counting

score 911 · Answer 1 · 2026-04-16 12:24:15

911

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Proving $\sum_{k=1}^{n} k \binom{n}{k} = n \cdot 2^{n-1}$ by double counting

Published on 16 Apr 2026 - 12:24

score 70 · Answer 2 · 2026-04-15 06:09:06

70

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Number of ways to form 3 digit numbers from 1,2,5,6,8 if each digit can only be used once.

Published on 15 Apr 2026 - 6:09

score 1.6k · Answer 3 · 2026-04-14 19:58:14

1.6k

Views

How many ways can 6 boys and 4 girls stand in a row if the girls must not be together?

Published on 14 Apr 2026 - 19:58

score 283 · Answer 4 · 2026-05-10 14:48:47

283

Views

Vishnoi's Proof of Combinatorial Nullstellensatz

Published on 10 May 2026 - 14:48

score 37 · Answer 5 · 2026-04-09 16:53:04

37

Views

counting ways for sum with maximums on variables

Published on 09 Apr 2026 - 16:53

score 183 · Answer 6 · 2026-04-10 07:20:23

183

Views

Permutation of array.

Published on 10 Apr 2026 - 7:20

score 58 · Answer 7 · 2026-05-01 00:23:00

58

Views

How to prove these two derangement number formulas are equivalent?

Published on 01 May 2026 - 0:23

score 619 · Answer 8 · 2026-04-17 08:20:41

619

Views

Solve the recurrence relation $n(n-1)a_n - (n-2)^2a_{n-2}= 0$, $a_0=0$, $a_1=1$

Published on 17 Apr 2026 - 8:20

score 1.2k · Answer 9 · 2026-04-14 01:00:58

1.2k

Views

$n$ lines in a plane, proper coloring of intersection points with just 3 colors

Published on 14 Apr 2026 - 1:00

score 584 · Answer 10 · 2026-04-14 15:08:06

584

Views

Counting question on bit strings - problem with using cases

Published on 14 Apr 2026 - 15:08

score 49 · Answer 11 · 2026-04-17 05:43:20

Given 20 sugar bars and 50 salt bars. Consider subsets of these 70 bars, consisting of 30 bars, exactly 12 are sugar bars. How many such subsets?

score 2.4k · Answer 12 · 2026-04-14 09:30:27

2.4k

Views

Using Combinatorics for Dice

Published on 14 Apr 2026 - 9:30

score 41 · Answer 13 · 2026-04-11 23:03:25

41

Views

How many subsets are there for this case?

Published on 11 Apr 2026 - 23:03

score 250 · Answer 14 · 2026-04-11 01:04:44

250

Views

Discrete Math: Combination with Repetitions

Published on 11 Apr 2026 - 1:04

score 520 · Answer 15 · 2026-05-11 04:19:20

520

Views

How to find the average value/sum of combinations with repetitions

Published on 11 May 2026 - 4:19

List Question

Proving $\sum_{k=1}^{n} k \binom{n}{k} = n \cdot 2^{n-1}$ by double counting

Number of ways to form 3 digit numbers from 1,2,5,6,8 if each digit can only be used once.

How many ways can 6 boys and 4 girls stand in a row if the girls must not be together?

Vishnoi's Proof of Combinatorial Nullstellensatz

counting ways for sum with maximums on variables

Permutation of array.

How to prove these two derangement number formulas are equivalent?

Solve the recurrence relation $n(n-1)a_n - (n-2)^2a_{n-2}= 0$, $a_0=0$, $a_1=1$

$n$ lines in a plane, proper coloring of intersection points with just 3 colors

Counting question on bit strings - problem with using cases

Given 20 sugar bars and 50 salt bars. Consider subsets of these 70 bars, consisting of 30 bars, exactly 12 are sugar bars. How many such subsets?

Using Combinatorics for Dice

How many subsets are there for this case?

Discrete Math: Combination with Repetitions

How to find the average value/sum of combinations with repetitions

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