Problem 5 A carnival has four kissing booths set up with wom

Problem 5: A carnival has four kissing booths set up with women inside: Kelly, Brenda, Donna, and Andrea. Five men randomly choose a kissing booth. Find the probability that all women get at least one kiss. (8 points)

Solution

The total number of options the five men have is 4^5 = 1024.

**************

Now, to assure one kiss, we first permute the first 4 men to each of the 4 women. There are 4! = 24 such ways.

Now, the last man can choose any woman now. There are 4 such ways.

There are 5 ways to choose the last man.

Thus, the ways to get at least one kiss for each woman is 24*4*5 = 480.

************

Thus, the asked probability

P (all girls get at least one kiss) = 480/1024 = 0.46875 [ANSWER]