If each of n balls is placed at random in k urns, what is the probability...

If each of n balls is placed at random in k urns, what is the probability that exactly two urns remain empty?

Solutions

Expert Solution

Provided k<n

Total no. of ways each of n balls can be placed at random in k urns = kⁿ

Now consider that only the first two cells remain empty.

This can be achieved by first putting one ball in each of the remaining k-2 urns, and then placing the remaining n-(k-2)=n-k+2 balls in the k-2 urns in (k-2)^n-k+2 ways.

This event can happen for any two urns, which can be selected in ways.

Total no. of ways each of n balls can be placed at random in k urns in such a way that exactly 2 urns remain empty

orchestra answered 1 year ago

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