# CHALLENGE: Prove that Σ k * C[M,k] * C[(N-M),(n-k)] / C[N,n] = M*n/N?

Can anyone prove the following statement? (or falsify it if you don’t believe it?)
b
Σ k * C[M,k] * C[(N-M),(n-k)] / C[N,n] = M*n/N
k=a
a = max (0, n+M-N)
b = min (n, M)
N, M and n are any positive integral constants satisfying
N ≥ M, n (Є Z+)
k (not n) is the index variable.
C[i,j] = iCj =...
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Can anyone prove the following statement? (or falsify it if you don’t believe it?)

b

Σ k * C[M,k] * C[(N-M),(n-k)] / C[N,n] = M*n/N

k=a

a = max (0, n+M-N)

b = min (n, M)

N, M and n are any positive integral constants satisfying

N ≥ M, n (Є Z+)

k (not n) is the index variable.

C[i,j] = iCj = i!/[j!(i-j)!]

NOTE: The limits of the summation, a and b, are only intended to make the nCr function meaningful. k would normally go from 0 to n, but k must never exceed M, and n-k must never exceed N-M.

b

Σ k * C[M,k] * C[(N-M),(n-k)] / C[N,n] = M*n/N

k=a

a = max (0, n+M-N)

b = min (n, M)

N, M and n are any positive integral constants satisfying

N ≥ M, n (Є Z+)

k (not n) is the index variable.

C[i,j] = iCj = i!/[j!(i-j)!]

NOTE: The limits of the summation, a and b, are only intended to make the nCr function meaningful. k would normally go from 0 to n, but k must never exceed M, and n-k must never exceed N-M.

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