Greg, Marcia, Peter, Jan, Bobby, and Cindy are participating in a Secret Santas

Question

Greg, Marcia, Peter, Jan, Bobby, and Cindy are participating in a Secret Santas gift exchange. They have put their names in a hat, and each will randomly select a name from this hat. What is the probability that none of them will end up with his or her own name? Hence no re-selection is needed. What is the probability that exactly three of them will end up with their own names? Why would total re-selection be warranted in all cases except the case in which none of them end up which his or her own name?

Explanation / Answer

a)Probability that none of them gets their name = (1/1!) - (1/2!) + (1/3!) - (1/4!) + (1/5!) - (1/6!) = 1 - 1/2 + 1/6 - 1/24 + 1/120 - 1/720 = 1- 0.368 = 0.632 b) total number of possibilities = 6! possibilities in which 3 of them get their names = 6C3 * 2 = 40 so probability = 40/6! = 0.055 c) sorry i dint understand the C part, i can answer it if u explain it in comment below, and please rate my answer.

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