Question

The local Scout group has 12 scouts. Each Christmas, they do a secret santa as part of the end of year break-up party. Each scout brings in a single wrapped present to put into a pile, and then each scout chooses a present from the pile which they unwrap and take home. Suppose the scouts choose their presents completely at random. (a) Determine the probability that no scout takes home the present they brought. (b) Determine the probability that at least three scouts each take home the present they brought. (c) Two of the scouts are brothers named Tom and Will, and they are the only members of their family in the scout group. Determine the probability that the two presents that Tom and Will contributed to the pile come back home with them.

Answer 1