Question

A ballroom dancing class has 20 men and 24 women. Five pairs are to be chosen, each consisting of one man and one woman, and no individual can be included in more than one pair.1 How many different ways can the 5 pairs be chosen

Answer 1

`7.908* 10^(10)`

Explanation:

Total number of mens=20

Total number of women=24

Number of pairs are to be chosen =5

We have to find the number of different ways can the 5 pairs be chosen.

5 Pairs included 5 women and 5 men.

Therefore, number of ways in which 5 pairs can be chosen=
`20C_5* 24C_5* 5!`

Formula:
`nC_r=(n!)/(r!(n-r)!)`

Number of ways in which 5 pairs can be chosen=
`(20!)/(5!15!)* (24!)/(5!19!)* 5!`

Number of ways in which 5 pairs can be chosen=
`7.908* 10^(10)`