Finite Math Examples

${}_{6}P_{5}$

Step 1

Evaluate ${}_{6}P_{5}$ using the formula ${}_{n}P_{r} = \frac{n!}{(n - r)!}$ .

$\frac{6!}{(6 - 5)!}$

Step 2

Subtract $5$ from $6$ .

$\frac{6!}{(1)!}$

Step 3

Simplify $\frac{6!}{(1)!}$ .

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Step 3.1

Simplify the numerator.

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Step 3.1.1

Expand $6!$ to $6 \cdot 5 \cdot 4 \cdot 3 \cdot 2 \cdot 1$ .

$\frac{6 \cdot 5 \cdot 4 \cdot 3 \cdot 2 \cdot 1}{(1)!}$

Step 3.1.2

Multiply $6 \cdot 5 \cdot 4 \cdot 3 \cdot 2 \cdot 1$ .

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Step 3.1.2.1

Multiply $6$ by $5$ .

$\frac{30 \cdot 4 \cdot 3 \cdot 2 \cdot 1}{(1)!}$

Step 3.1.2.2

Multiply $30$ by $4$ .

$\frac{120 \cdot 3 \cdot 2 \cdot 1}{(1)!}$

Step 3.1.2.3

Multiply $120$ by $3$ .

$\frac{360 \cdot 2 \cdot 1}{(1)!}$

Step 3.1.2.4

Multiply $360$ by $2$ .

$\frac{720 \cdot 1}{(1)!}$

Step 3.1.2.5

Multiply $720$ by $1$ .

$\frac{720}{(1)!}$

Step 3.2

Expand $(1)!$ to $1$ .

$\frac{720}{1}$

Step 3.3

Divide $720$ by $1$ .

$720$