Finite Math Examples

${}_{6}P_{2}$

Find the number of possible ordered permutations when $r$ items are selected from $n$ available items.

${}_{6}P_{2} = {}_{n}P_{r} = \frac{n!}{(n - r)!}$

Fill in the known values.

$\frac{6!}{(6 - 2)!}$

Simplify.

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Subtract $2$ from $6$ .

$\frac{6!}{4!}$

Rewrite $6!$ as $6 \cdot 5 \cdot 4!$ .

$\frac{6 \cdot 5 \cdot 4!}{4!}$

Reduce the expression by cancelling the common factors.

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Cancel the common factor.

$\frac{6 \cdot 5 \cdot 4!}{4!}$

Divide $6 \cdot 5$ by $1$ .

$6 \cdot 5$

Multiply $6$ by $5$ .

$30$

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