One way that large families often decide who will give each other Christmas presents is to do a drawing. All the names go in a hat and each person draws a name and that is the person to whom he or she gives a gift. The problem with this method is that there is a chance that one or more people will draw their own names. The following table gives the probabilities that X people in a family of 4 will draw their own names in this process.

a. What is the probability that nobody will draw his or her own names? 

b. What is the probability that at least one person will draw his or her name? 

c. Explain why an outcome of exactly 3 matches is impossible.

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p(x) 0 9/24 1 8/24 2 6/24 3 0 4 1/24