Question

There are five members on a student council. Two of these members will serve on a spring formal committee. How many possible spring formal committees are there

Answer 1

Answer:

10

Step-by-step explanation:

Given that:

There are a total of 5 members on a student council.

2 of these members will serve in Spring Formal Committee.

To find:

How many possible spring formal committees can be there ?

Solution:

If the observe this problem closely, we are actually asked nothing but the number of ways to select 2 members out of 5.

This is a simple selection problem in which we have to find the number of ways to select $r$ objects out of $n$.

The number of ways = $_nC_r =\frac {n!}{r!(n-r)!}$

Here,

$n = 5\\r=2$

Hence, the required number of ways are:

$_5C_2 =\frac {5!}{2!(5-2)!}\\\Rightarrow \dfrac {5!}{2!3!} = \dfrac {5\times 4\times 3!}{2!3!}\\\Rightarrow \dfrac {5\times 4}{2} = \dfrac{20}{2}\\\Rightarrow \bold{10}$

So, the number of possible spring formal committees are 10.