This is Chance strategy and choice problem 19.9

19.9 Assume that we are given M possible labels and a people. Let p,, be the probability that at least two people have the same label. Show that p. = 1 -q., where q = probability that no two people have the same label, is given by M . (M- 1) .. .(M-n+2) . . . (M-n+1) Apply the result to address the following problems: (a) Find the probability p that at least two people of four were born on the same day of the week. (b) Find the probability that in a group of 10, at least 2 were born in the same month. (c) Find the minimum number of people so that the probability p that two were born in the same month satisfies p > 1/2