Interesting problem I found, and can't solve it since the morning:

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> We have $n$ keys and $n$ piggy banks. Each key fits only one piggy bank. We randomly put exactly one key in each piggy bank. Then we randomly shatter $1\le k\le n$ piggy banks. What is the probability that we are able to open all other piggy banks?
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Really interested me. I thought about approach with cycles in permutation. When we number all piggy banks and their keys with numbers $1...n$ and then denote $f(i)$ - the number of key that is in $i$-th piggy bank then we have permutation $f$. So to open all piggy banks we need at least one key from each cycle in permutation $f$. But I completely don't know how to count it. Can anybody help?