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1. ### Pascal's triangle identity?

...fit the defining Pascal's Triangle property: C(m,k) + C(m,k-1) = C(m+1,k) [0 < k <= m].  ...

1 Answers · Science & Mathematics · 09/02/2020

2. ### Pigeonhole principle - hard math problems?

...integer. Therefore, if we choose k (k > ceiling(k/2)) integers from T then at least two ...y∈S such that a≠b, {a,b}≠{x,y} and b−a=y−x. c. Let S = {s1,s2, ... ,sk} and s1<...

1 Answers · Science & Mathematics · 09/02/2020

3. ### Proof of combinatorics identity?

... (x+n+1)Cn .    We know mCk = (m-1)Ck + (m-1)C(k-1) because  mCk  = m! / [(m-k)!k!]  = (m-1)!*m / [(m-k)!k!]  = (m-1)!*((m-k...

2 Answers · Science & Mathematics · 08/02/2020

4. ### pigeonhole principle - prove that, if n>(m+k−1)C(k−1)?

... 6C2 = 15 ways.    In general, there are (m+k-1)C(k-1) ways. So if n > (m+k-1)C(k-1)  then at least 2 ...

1 Answers · Science & Mathematics · 06/02/2020

5. ### Variance X - Y?

...(B) - 2 Cov(A,B). c) then you have to relate the given correlation to the covariance...). d) then you have to apply Var(kB) = k^2 Var(B). (variance of a constant times a...

1 Answers · Science & Mathematics · 23/10/2019

6. ### Combinatorics And Even Numbers?

... , assume that (#1) stands when m = k . That is , "(2^k)C(1), (2^k)C(2), ... , (2^k)C(2^k-1) are all even" ---(#2...

2 Answers · Science & Mathematics · 03/10/2019