Question

A club of twenty students wants to pick a three person subcommittee. How many ways can this be done?

Answer 1

`1140`

Explanation:

Combinations : If we want to choose
`r` items out of
`n` items, and order of the selection does not matter.

possible ways
`=^nc_(r)=(n!)/(r!(n-r)!)`

Total number of students
`=20`

Persons in subcommittee
`=3`

Here order of selection does not matter, so we can use combination to get possible number of ways.

Number of ways
`=^(20)c_(3)=(20!)/((20-3)!3!)`

`=(20!)/(17!* 3!)=(20* 19* 18* 17!)/(17!* 3!)\\\\=(20* 19* 18)/(6)\\\\=20* 19* 3\\\\=1140`