Finite Math Examples

${}_{6}P_{4}$

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

${}_{6}P_{4} = {}_{n}P_{r} = \frac{n!}{(n - r)!}$

Fill in the known values.

$\frac{6!}{(6 - 4)!}$

Simplify.

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Subtract $4$ from $6$ .

$\frac{6!}{2!}$

Rewrite $6!$ as $6 \cdot 5 \cdot 4 \cdot 3 \cdot 2!$ .

$\frac{6 \cdot 5 \cdot 4 \cdot 3 \cdot 2!}{2!}$

Reduce the expression by cancelling the common factors.

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Cancel the common factor.

$\frac{6 \cdot 5 \cdot 4 \cdot 3 \cdot 2!}{2!}$

Divide $6 \cdot 5 \cdot 4 \cdot 3$ by $1$ .

$6 \cdot 5 \cdot 4 \cdot 3$

Multiply.

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Multiply $6$ by $5$ .

$30 \cdot 4 \cdot 3$

Multiply $30$ by $4$ .

$120 \cdot 3$

Multiply $120$ by $3$ .

$360$

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