I think it should be

P(C) = ((n-k) over r) (1/5)^r * (1 - 1/5)^(n-k-r)

E[C]=((n-k) over r) (1/5)^r * (1 - 1/5)^(n-k-r)*1

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Abstract algebra continues the conceptual developments of linear algebra, on an even grander scale.

Dr. Paul Garrett