Question

Fifteen married couples are at a dance lesson. Assume that (male-female) dance pairs are assigned at random. (a) What is the number of possible assignments? (b) What is the probability that each husband ends up dancing with his wife?

Answer 1

A)225, b) 1/ 4.3789389e17

Explanation:

The product rule says that if there are N ways of doing something and M ways of doing another thing, the number of ways of doing both things is equal to NxM

In a party of 15 males and 15 females the possible combination of pairing one male to a female is

15 x 15 = 225

The probability that each husband ends up dancing with his wife can be express as

Prhusband 1 pair wife 1 = 1/15

Pr husband 2 pair wife 2 = 1/15

PR husband 3 pair wife 3 = 1/15

Same for all

Therefore the probability of each husband paired with his wife is

1/15 and 1/15 and 1/15 and 1/15 and 1/15 and 1/15 and 1/15 and 1/15 and 1/15 and 1/15 and 1/15 and 1/15 and 1/15 and 1/15 and 1/15

Which implies

1/15 x 1/15 x 1/15 x 1/15x 1/15 x 1/15 x 1/15x 1/15 x 1/15 x 1/15x 1/15 x 1/15 x 1/15x 1/15 x 1/15 = 1/ 4.3789389e17

=