Question

How many ways are there to select a committee of five from a club with 30 members?

Answer 1

Answer: 142506

Explanation:

To select a committee we don't require any order , so we use a combination.

The number of combinations of selecting r things out of n things:

`^nC_r=(n!)/(r!(n-r)!)`

So, the number of combinations of selecting 5 members out of 30 =
`(30!)/(5!(30-5)!)=(30*29*28*27*26*25!)/(120*5!)=142506`

Hence, total number of ways= 142506