Question

A) A club is considering changing its bylaws. In an initial straw vote on the issue, 24 of the 40 members of the club favored the change and 16 did not. A committee of six is to be chosen from the 40 club members to devote further study to the issue. a) How many committees of six can be formed from the club membership

Answer 1

38,38,380

Explanation:

GIVEN: A club is considering changing its laws. In an initial straw vote on the issue,
`24` of the
`40` members of the club favored the change and
`16` did not. A committee of six is to be chosen from the
`40` club members to devote further study to the issue.

TO FIND: How many committees of six can be formed from the club membership.

SOLUTION:

Total number of members
`=40`

Total members to be chosen
`=6`

To select committee of
`6` members from
`40`
`=^(40)C_6`

`=(40!)/(34!6!)`

`=38,38,380`

Hence 38,38,380 different committee can be formed.