Finite Math Examples

52 P 5

${}_{52}P_{5}$

Step 1

Evaluate

52 P 5

${}_{52}P_{5}$ using the formula

n P r = \frac{n!}{(n - r)!}

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

\frac{52!}{(52 - 5)!}

$\frac{52!}{(52 - 5)!}$

Step 2

Subtract

5

$5$ from

52

$52$ .

\frac{52!}{(47)!}

$\frac{52!}{(47)!}$

Step 3

Simplify

\frac{52!}{(47)!}

$\frac{52!}{(47)!}$ .

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Step 3.1

Rewrite

52!

$52!$ as

52 \cdot 51 \cdot 50 \cdot 49 \cdot 48 \cdot 47!

$52 \cdot 51 \cdot 50 \cdot 49 \cdot 48 \cdot 47!$ .

\frac{52 \cdot 51 \cdot 50 \cdot 49 \cdot 48 \cdot 47!}{(47)!}

$\frac{52 \cdot 51 \cdot 50 \cdot 49 \cdot 48 \cdot 47!}{(47)!}$

Step 3.2

Cancel the common factor of

47!

$47!$ .

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Step 3.2.1

Cancel the common factor.

$\frac{52 \cdot 51 \cdot 50 \cdot 49 \cdot 48 \cdot 47!}{(47)!}$

Step 3.2.2

Divide

$52 \cdot 51 \cdot 50 \cdot 49 \cdot 48$ by

$1$ .

$52 \cdot 51 \cdot 50 \cdot 49 \cdot 48$

Step 3.3

Multiply

$52 \cdot 51 \cdot 50 \cdot 49 \cdot 48$ .

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Step 3.3.1

Multiply

$52$ by

$51$ .

$2652 \cdot 50 \cdot 49 \cdot 48$

Step 3.3.2

Multiply

$2652$ by

$50$ .

$132600 \cdot 49 \cdot 48$

Step 3.3.3

Multiply

$132600$ by

$49$ .

$6497400 \cdot 48$

Step 3.3.4

Multiply

$6497400$ by

$48$ .

$311875200$

${}_{52}P_{5}$

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