Finite Math Examples

${}_{10}P_{9}$

Step 1

Evaluate ${}_{10}P_{9}$ using the formula ${}_{n}P_{r} = \frac{n!}{(n - r)!}$ .

$\frac{10!}{(10 - 9)!}$

Step 2

Subtract $9$ from $10$ .

$\frac{10!}{(1)!}$

Step 3

Simplify $\frac{10!}{(1)!}$ .

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Step 3.1

Simplify the numerator.

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Step 3.1.1

Expand $10!$ to $10 \cdot 9 \cdot 8 \cdot 7 \cdot 6 \cdot 5 \cdot 4 \cdot 3 \cdot 2 \cdot 1$ .

$\frac{10 \cdot 9 \cdot 8 \cdot 7 \cdot 6 \cdot 5 \cdot 4 \cdot 3 \cdot 2 \cdot 1}{(1)!}$

Step 3.1.2

Multiply $10 \cdot 9 \cdot 8 \cdot 7 \cdot 6 \cdot 5 \cdot 4 \cdot 3 \cdot 2 \cdot 1$ .

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Step 3.1.2.1

Multiply $10$ by $9$ .

$\frac{90 \cdot 8 \cdot 7 \cdot 6 \cdot 5 \cdot 4 \cdot 3 \cdot 2 \cdot 1}{(1)!}$

Step 3.1.2.2

Multiply $90$ by $8$ .

$\frac{720 \cdot 7 \cdot 6 \cdot 5 \cdot 4 \cdot 3 \cdot 2 \cdot 1}{(1)!}$

Step 3.1.2.3

Multiply $720$ by $7$ .

$\frac{5040 \cdot 6 \cdot 5 \cdot 4 \cdot 3 \cdot 2 \cdot 1}{(1)!}$

Step 3.1.2.4

Multiply $5040$ by $6$ .

$\frac{30240 \cdot 5 \cdot 4 \cdot 3 \cdot 2 \cdot 1}{(1)!}$

Step 3.1.2.5

Multiply $30240$ by $5$ .

$\frac{151200 \cdot 4 \cdot 3 \cdot 2 \cdot 1}{(1)!}$

Step 3.1.2.6

Multiply $151200$ by $4$ .

$\frac{604800 \cdot 3 \cdot 2 \cdot 1}{(1)!}$

Step 3.1.2.7

Multiply $604800$ by $3$ .

$\frac{1814400 \cdot 2 \cdot 1}{(1)!}$

Step 3.1.2.8

Multiply $1814400$ by $2$ .

$\frac{3628800 \cdot 1}{(1)!}$

Step 3.1.2.9

Multiply $3628800$ by $1$ .

$\frac{3628800}{(1)!}$

Step 3.2

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

$\frac{3628800}{1}$

Step 3.3

Divide $3628800$ by $1$ .

$3628800$