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A random permutation of n objects is selected. (a) What is the probability that no pair...

A random permutation of n objects is selected.

(a) What is the probability that no pair of objects lies in their initial positions (either exactly as they were or swapped) if n =3?

(b) What is the probability that no pair of objects lies in their initial positions (either exactly as they were or swapped) if n =4?

(c) Let n be an even number, say n D 2k. Let L be the (random) number of odd-numbered objects that are placed in odd-numbered positions. Give the name of the distribution of L, including all parameters. Also state the mean and variance of L.

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