Question

What at the chances of getting 20 heads on a row if tossed 100 million times?

score 1k · Answer 1 · 2016-07-13 10:49:11

1k

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What at the chances of getting 20 heads on a row if tossed 100 million times?

Published on 13 Jul 2016 - 10:49

score 1.2k · Answer 2 · 2016-07-17 21:31:58

1.2k

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Combinatorial proof of $\sum_{k=0}^{n}(-1)^{k}\binom{n}{k}(l-k)^n=n!$, using inclusion-exclusion

Published on 17 Jul 2016 - 21:31

score 125 · Answer 3 · 2026-03-27 03:42:25

125

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Elementary proof for average number of tree components in a random forest of fixed size

Published on 27 Mar 2026 - 3:42

score 3.5k · Answer 4 · 2016-07-29 11:22:50

3.5k

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How to show $\sum_{k=0}^{n}\binom{n+k}{k}\frac{1}{2^k}=2^{n}$

Published on 29 Jul 2016 - 11:22

score 889 · Answer 5 · 2016-08-02 23:14:33

889

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Prove ${n \choose k}^2 = \sum_{i=0}^{k}{n \choose i}{n-i \choose k-i}{n-k \choose k-i}$ using a combinatorial argument

Published on 02 Aug 2016 - 23:14

score 119 · Answer 6 · 2016-08-06 12:13:25

119

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Is there a combinatorial interpretation for the following sum?

Published on 06 Aug 2016 - 12:13

score 936 · Answer 7 · 2016-08-22 23:47:26

936

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Combinatorial proofs of the following identities

Published on 22 Aug 2016 - 23:47

score 548 · Answer 8 · 2016-09-07 00:53:36

548

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Combinatorial proof of a binomial identity: $\sum_k \binom {2r} {2k-1}\binom{k-1}{s-1} = 2^{2r-2s+1}\binom{2r-s}{s-1}$

Published on 07 Sep 2016 - 0:53

score 1.2k · Answer 9 · 2016-09-14 10:01:01

1.2k

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Prove the identity $ \sum_{i=0}^n {n \choose i} i = n2^{n-1} $ using combinatorial proof.

Published on 14 Sep 2016 - 10:01

score 5k · Answer 10 · 2016-09-14 10:30:01

5k

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Prove the identity $\sum_{k=0}^n \binom{n}{k}=2^n.$ using combinatorial proof

Published on 14 Sep 2016 - 10:30

score 74 · Answer 11 · 2016-09-16 12:33:43

74

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Are these two summation expressions equal to each other?

Published on 16 Sep 2016 - 12:33

score 133 · Answer 12 · 2016-09-21 15:19:51

133

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How to show the following identity?

Published on 21 Sep 2016 - 15:19

score 1k · Answer 13 · 2016-09-23 18:45:00

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$\sum_{k=-m}^{n} \binom{m+k}{r} \binom{n-k}{s} =\binom{m+n+1}{r+s+1}$ using Counting argument

Published on 23 Sep 2016 - 18:45

score 204 · Answer 14 · 2016-09-25 23:23:49

204

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Summation of binomial with factor squared $\sum_{k=0}^n k^2 \binom nk^2 = n^2 {2n-2 \choose n-1}$

Published on 25 Sep 2016 - 23:23

score 266 · Answer 15 · 2016-09-29 05:24:44

266

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Proof of Binomial Sum via Double Counting

Published on 29 Sep 2016 - 5:24

List Question

What at the chances of getting 20 heads on a row if tossed 100 million times?

Combinatorial proof of $\sum_{k=0}^{n}(-1)^{k}\binom{n}{k}(l-k)^n=n!$, using inclusion-exclusion

Elementary proof for average number of tree components in a random forest of fixed size

How to show $\sum_{k=0}^{n}\binom{n+k}{k}\frac{1}{2^k}=2^{n}$

Prove ${n \choose k}^2 = \sum_{i=0}^{k}{n \choose i}{n-i \choose k-i}{n-k \choose k-i}$ using a combinatorial argument

Is there a combinatorial interpretation for the following sum?

Combinatorial proofs of the following identities

Combinatorial proof of a binomial identity: $\sum_k \binom {2r} {2k-1}\binom{k-1}{s-1} = 2^{2r-2s+1}\binom{2r-s}{s-1}$

Prove the identity $ \sum_{i=0}^n {n \choose i} i = n2^{n-1} $ using combinatorial proof.

Prove the identity $\sum_{k=0}^n \binom{n}{k}=2^n.$ using combinatorial proof

Are these two summation expressions equal to each other?

How to show the following identity?

$\sum_{k=-m}^{n} \binom{m+k}{r} \binom{n-k}{s} =\binom{m+n+1}{r+s+1}$ using Counting argument

Summation of binomial with factor squared $\sum_{k=0}^n k^2 \binom nk^2 = n^2 {2n-2 \choose n-1}$

Proof of Binomial Sum via Double Counting

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