Question

How many subcommittees of 5 people can be formed from a committee consisting of 8 people

Answer 1

56 subcommittees of 5 people can be formed from a committee consisting of 8 people

Given :

The subcommittees of 5 people are to be formed from a committee consisting of 8 people

To find :

The number of subcommittees

Solution :

Step 1 of 2 :

Write down the number of people in the committee

Here it is given that the committee consists of 8 people

Step 2 of 2 :

Find the number of subcommittees

Since the subcommittees of 5 people are to be formed from a committee consisting of 8 people

Hence the required number of subcommittees

$\displaystyle \sf{ = {}^{8}C_5 }$

$\displaystyle \sf{ = \frac{8!}{5! \: (8 - 5)!} }$

$\displaystyle \sf{ = \frac{8!}{5! \:3!} }$

$\displaystyle \sf{ = \frac{8 \times 7 \times 6 \times 5!}{5! \times \:(3 \times 2 \times 1)} }$

$\displaystyle \sf{ = \frac{8 \times 7 \times 6 }{6} }$

$\displaystyle \sf{ = 56 }$

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