Consider a group of n people who have n distinct names. We ask m of them, one at

Question

Consider a group of n people who have n distinct names. We ask m of them, one at the time, to tell us their names. The way we select them and the order we choose them is completely random. Also, we never ask the same person twice.

a) For n = m = 3, what is the probability that the names are all in alphabetical order?
b) For n = m = 8, what is the probability that the names are all in alphabetical order?
c) For n = 20 and m = 10, what is the probability that the 10 names are all in alphabetical order?

Explanation / Answer

a)total number of ways of selecting 3 out of 3 manes and arranging them in order=3P3 =6

as number of way these can be arranged in alphabetical order =3C3 =1

henceprobability that the names are all in alphabetical order =1/6

b)

probability that the names are all in alphabetical order =8C8 /8P8 =1/8! =1/40320

c)

probability that the 10 names are all in alphabetical order =20C10 /20P10 =1/3628800

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