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?

A) 225, b) 1 / 4.3789389e17

Step-by-step 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

=