Question

There is money to send four of nine city council members to a conference in Honolulu. All want to go, so they decide to choose the members to go to the conference by a random process. How many different combinations of four council members can be selected from the nine who want to go to the conference

Answer 1

126

Explanation:

There are 9 city council members.

We have to choose 4 of them.

We have to use the combination as :

`$^9C_4$`

where, 9 is the population size

4 is the sample size.

Therefore, the total number of possible samples without replacement is given as :

`$^9C_4=(9!)/(4!(9-4)!)$`

`$=(9!)/(5! \ 4!)$`

`$=(9 * 8 * 7 * 6)/(4 * 3 * 2 * 1)$`

= 126