Finite Math Examples

${}_{28}P_{9}$

Step 1

Evaluate ${}_{28}P_{9}$ using the formula ${}_{n}P_{r} = \frac{n!}{(n - r)!}$ .

$\frac{28!}{(28 - 9)!}$

Step 2

Subtract $9$ from $28$ .

$\frac{28!}{(19)!}$

Step 3

Simplify $\frac{28!}{(19)!}$ .

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Step 3.1

Rewrite $28!$ as $28 \cdot 27 \cdot 26 \cdot 25 \cdot 24 \cdot 23 \cdot 22 \cdot 21 \cdot 20 \cdot 19!$ .

$\frac{28 \cdot 27 \cdot 26 \cdot 25 \cdot 24 \cdot 23 \cdot 22 \cdot 21 \cdot 20 \cdot 19!}{(19)!}$

Step 3.2

Cancel the common factor of $19!$ .

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Step 3.2.1

Cancel the common factor.

$\frac{28 \cdot 27 \cdot 26 \cdot 25 \cdot 24 \cdot 23 \cdot 22 \cdot 21 \cdot 20 \cdot 19!}{(19)!}$

Step 3.2.2

Divide $28 \cdot 27 \cdot 26 \cdot 25 \cdot 24 \cdot 23 \cdot 22 \cdot 21 \cdot 20$ by $1$ .

$28 \cdot 27 \cdot 26 \cdot 25 \cdot 24 \cdot 23 \cdot 22 \cdot 21 \cdot 20$

Step 3.3

Multiply $28 \cdot 27 \cdot 26 \cdot 25 \cdot 24 \cdot 23 \cdot 22 \cdot 21 \cdot 20$ .

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Step 3.3.1

Multiply $28$ by $27$ .

$756 \cdot 26 \cdot 25 \cdot 24 \cdot 23 \cdot 22 \cdot 21 \cdot 20$

Step 3.3.2

Multiply $756$ by $26$ .

$19656 \cdot 25 \cdot 24 \cdot 23 \cdot 22 \cdot 21 \cdot 20$

Step 3.3.3

Multiply $19656$ by $25$ .

$491400 \cdot 24 \cdot 23 \cdot 22 \cdot 21 \cdot 20$

Step 3.3.4

Multiply $491400$ by $24$ .

$11793600 \cdot 23 \cdot 22 \cdot 21 \cdot 20$

Step 3.3.5

Multiply $11793600$ by $23$ .

$271252800 \cdot 22 \cdot 21 \cdot 20$

Step 3.3.6

Multiply $271252800$ by $22$ .

$5967561600 \cdot 21 \cdot 20$

Step 3.3.7

Multiply $5967561600$ by $21$ .

$125318793600 \cdot 20$

Step 3.3.8

Multiply $125318793600$ by $20$ .

$2506375872000$