Question

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

Answer 1

Answer: 142506

Step-by-step 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:

$^nC_r=\dfrac{n!}{r!(n-r)!}$

So, the number of combinations of selecting 5 members out of 30 = $\dfrac{30!}{5!(30-5)!}=\dfrac{30\times29\times28\times27\times26\times25!}{120\times5!}=142506$

Hence, total number of ways= 142506