Question

There are 8 members on the student council. A committee consisting of 2 members is to be made. How many different committees are possible.

Answer 1

28 committees

Step-by-step explanation:

The total number of members = 8

We want to make a committee of 2 members

We will be applying the combination concept

`\begin{gathered} \text{let n = 8 and r = 2} \\ ^nC_r\text{ = }\frac{n!}{(n\text{ - r)!r!}} \\ ^8C_2\text{ = }\frac{8!}{(8\text{ - 2)!2!}} \\ ^8C_2\text{ = }(8!)/(6!2!) \\ ^(8_2)C\text{ = }\frac{8\text{ x 7 x 6 x 5 x 4 x 3 x 2 x 1}}{6\text{ x 5 x 4 x 3 x 2 x 1! 2 x 1}} \\ ^{8_{}}C_2\text{ = }\frac{8\cdot\text{ 7}}{2} \\ ^{8_{}}C_2\text{ = 28 committees} \end{gathered}`

Therefore, 28 committees can be formed