How many ways can you select a committee of five members from a group of 10 people?

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How many ways can you select a committee of five members from a group of 10 people?

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Answer 1 · 2018-03-24T16:28:46

There are $252$ $252$ ways to select a committee of five members from a group of $10$ $10$ people.

Explanation:

The number of ways to select $b$ $b$ people from a total of $a$ $a$ people is $\frac{a!}{b! \cdot (a - b)!}$ $(a!)/(b!*(a-b)!$ .

Plugging in $10$ $10$ for $a$ $a$ and $5$ $5$ for $b$ $b$ :
$P = \frac{10!}{5! (10 - 5)!}$ $P = (10!)/(5!(10-5)!)$
$P = \frac{3628800}{120 \cdot 5!}$ $P = 3628800/(120*5!)$
$P = \frac{3628800}{14400}$ $P = 3628800/14400$
$P = 252$ $P = 252$

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How many ways can you select a committee of five members from a group of 10 people?

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