Question

Choose the method to solve the problem below: There are members on a board of directors. If they must form a subcommittee of members, how many different subcommittees are possible?

a. 512
b. 56
c. 6
d. 336

Answer 1

b. 56

Explanation:

Please consider the complete question.

There are 8 members on a board of directors. If they must form a subcommittee of 3 members, how many different subcommittees are possible?

We will use combinations for solve our given problem.

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

n = Number of total items,

r = Items being chosen at a time.

For our given scenario
`n=8` and
`r=3`.

`^8C_3=(8!)/(3!(8-3)!)`

`^8C_3=(8!)/(3!\cdot 5!)`

`^8C_3=(8\cdot7\cdot6\cdot5!)/(3\cdot2\cdot1\cdot 5!)`

`^8C_3=8\cdot7`

`^8C_3=56`

Therefore, 56 different subcommittees are possible and option 'b' is the correct choice.