Suppose that there are 10 people in a party. Each person brings along a gift for exchange. The gifts are put in a pile and labeled with number 1 ~ 10. Each person in the party will randomly select one gift by picking slips of papers with numbers identifying the gifts.
What is the probability that there is at least one partygoer who ends up selecting his or her own gift?
My solution
Consider the complement of P(At least one)
We want to find P(None)=$\frac{9}{10}*\frac{8}{9}*\frac{7}{8}*\frac{6}{7}*\frac{5}{6}*\frac{4}{5}*\frac{3}{4}*\frac{2}{3}*\frac{1}{2}$
I am stuck. Help please!!!