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

Answer:

b. 56

Step-by-step 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.

$^nC_r=\frac{n!}{r!(n-r)!}$, where,

n = Number of total items,

r = Items being chosen at a time.

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

$^8C_3=\frac{8!}{3!(8-3)!}$

$^8C_3=\frac{8!}{3!\cdot 5!}$

$^8C_3=\frac{8\cdot7\cdot6\cdot5!}{3\cdot2\cdot1\cdot 5!}$

$^8C_3=8\cdot7$

$^8C_3=56$

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