Finite Math Examples

${}_{13}P_{10}$

Step 1

Evaluate ${}_{13}P_{10}$ using the formula ${}_{n}P_{r} = \frac{n!}{(n - r)!}$ .

$\frac{13!}{(13 - 10)!}$

Step 2

Subtract $10$ from $13$ .

$\frac{13!}{(3)!}$

Step 3

Simplify $\frac{13!}{(3)!}$ .

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Step 3.1

Rewrite $13!$ as $13 \cdot 12 \cdot 11 \cdot 10 \cdot 9 \cdot 8 \cdot 7 \cdot 6 \cdot 5 \cdot 4 \cdot 3!$ .

$\frac{13 \cdot 12 \cdot 11 \cdot 10 \cdot 9 \cdot 8 \cdot 7 \cdot 6 \cdot 5 \cdot 4 \cdot 3!}{(3)!}$

Step 3.2

Cancel the common factor of $3!$ .

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Step 3.2.1

Cancel the common factor.

$\frac{13 \cdot 12 \cdot 11 \cdot 10 \cdot 9 \cdot 8 \cdot 7 \cdot 6 \cdot 5 \cdot 4 \cdot 3!}{(3)!}$

Step 3.2.2

Divide $13 \cdot 12 \cdot 11 \cdot 10 \cdot 9 \cdot 8 \cdot 7 \cdot 6 \cdot 5 \cdot 4$ by $1$ .

$13 \cdot 12 \cdot 11 \cdot 10 \cdot 9 \cdot 8 \cdot 7 \cdot 6 \cdot 5 \cdot 4$

Step 3.3

Multiply $13 \cdot 12 \cdot 11 \cdot 10 \cdot 9 \cdot 8 \cdot 7 \cdot 6 \cdot 5 \cdot 4$ .

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Step 3.3.1

Multiply $13$ by $12$ .

$156 \cdot 11 \cdot 10 \cdot 9 \cdot 8 \cdot 7 \cdot 6 \cdot 5 \cdot 4$

Step 3.3.2

Multiply $156$ by $11$ .

$1716 \cdot 10 \cdot 9 \cdot 8 \cdot 7 \cdot 6 \cdot 5 \cdot 4$

Step 3.3.3

Multiply $1716$ by $10$ .

$17160 \cdot 9 \cdot 8 \cdot 7 \cdot 6 \cdot 5 \cdot 4$

Step 3.3.4

Multiply $17160$ by $9$ .

$154440 \cdot 8 \cdot 7 \cdot 6 \cdot 5 \cdot 4$

Step 3.3.5

Multiply $154440$ by $8$ .

$1235520 \cdot 7 \cdot 6 \cdot 5 \cdot 4$

Step 3.3.6

Multiply $1235520$ by $7$ .

$8648640 \cdot 6 \cdot 5 \cdot 4$

Step 3.3.7

Multiply $8648640$ by $6$ .

$51891840 \cdot 5 \cdot 4$

Step 3.3.8

Multiply $51891840$ by $5$ .

$259459200 \cdot 4$

Step 3.3.9

Multiply $259459200$ by $4$ .

$1037836800$