Finite Math Examples

${}_{36}C_{9}$

Step 1

Evaluate ${}_{36}C_{9}$ using the formula ${}_{n}C_{r} = \frac{n!}{(n - r)! r!}$ .

$\frac{36!}{(36 - 9)! 9!}$

Step 2

Subtract $9$ from $36$ .

$\frac{36!}{(27)! 9!}$

Step 3

Simplify $\frac{36!}{(27)! 9!}$ .

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Step 3.1

Rewrite $36!$ as $36 \cdot 35 \cdot 34 \cdot 33 \cdot 32 \cdot 31 \cdot 30 \cdot 29 \cdot 28 \cdot 27!$ .

$\frac{36 \cdot 35 \cdot 34 \cdot 33 \cdot 32 \cdot 31 \cdot 30 \cdot 29 \cdot 28 \cdot 27!}{(27)! 9!}$

Step 3.2

Cancel the common factor of $27!$ .

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Step 3.2.1

Cancel the common factor.

$\frac{36 \cdot 35 \cdot 34 \cdot 33 \cdot 32 \cdot 31 \cdot 30 \cdot 29 \cdot 28 \cdot 27!}{(27)! 9!}$

Step 3.2.2

Rewrite the expression.

$\frac{36 \cdot 35 \cdot 34 \cdot 33 \cdot 32 \cdot 31 \cdot 30 \cdot 29 \cdot 28}{9!}$

Step 3.3

Simplify the numerator.

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Step 3.3.1

Multiply $36$ by $35$ .

$\frac{1260 \cdot 34 \cdot 33 \cdot 32 \cdot 31 \cdot 30 \cdot 29 \cdot 28}{9!}$

Step 3.3.2

Multiply $1260$ by $34$ .

$\frac{42840 \cdot 33 \cdot 32 \cdot 31 \cdot 30 \cdot 29 \cdot 28}{9!}$

Step 3.3.3

Multiply $42840$ by $33$ .

$\frac{1413720 \cdot 32 \cdot 31 \cdot 30 \cdot 29 \cdot 28}{9!}$

Step 3.3.4

Multiply $1413720$ by $32$ .

$\frac{45239040 \cdot 31 \cdot 30 \cdot 29 \cdot 28}{9!}$

Step 3.3.5

Multiply $45239040$ by $31$ .

$\frac{1402410240 \cdot 30 \cdot 29 \cdot 28}{9!}$

Step 3.3.6

Multiply $1402410240$ by $30$ .

$\frac{42072307200 \cdot 29 \cdot 28}{9!}$

Step 3.3.7

Multiply $42072307200$ by $29$ .

$\frac{1220096908800 \cdot 28}{9!}$

Step 3.3.8

Multiply $1220096908800$ by $28$ .

$\frac{34162713446400}{9!}$

Step 3.4

Simplify the denominator.

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Step 3.4.1

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

$\frac{34162713446400}{9 \cdot 8 \cdot 7 \cdot 6 \cdot 5 \cdot 4 \cdot 3 \cdot 2 \cdot 1}$

Step 3.4.2

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

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Step 3.4.2.1

Multiply $9$ by $8$ .

$\frac{34162713446400}{72 \cdot 7 \cdot 6 \cdot 5 \cdot 4 \cdot 3 \cdot 2 \cdot 1}$

Step 3.4.2.2

Multiply $72$ by $7$ .

$\frac{34162713446400}{504 \cdot 6 \cdot 5 \cdot 4 \cdot 3 \cdot 2 \cdot 1}$

Step 3.4.2.3

Multiply $504$ by $6$ .

$\frac{34162713446400}{3024 \cdot 5 \cdot 4 \cdot 3 \cdot 2 \cdot 1}$

Step 3.4.2.4

Multiply $3024$ by $5$ .

$\frac{34162713446400}{15120 \cdot 4 \cdot 3 \cdot 2 \cdot 1}$

Step 3.4.2.5

Multiply $15120$ by $4$ .

$\frac{34162713446400}{60480 \cdot 3 \cdot 2 \cdot 1}$

Step 3.4.2.6

Multiply $60480$ by $3$ .

$\frac{34162713446400}{181440 \cdot 2 \cdot 1}$

Step 3.4.2.7

Multiply $181440$ by $2$ .

$\frac{34162713446400}{362880 \cdot 1}$

Step 3.4.2.8

Multiply $362880$ by $1$ .

$\frac{34162713446400}{362880}$

Step 3.5

Divide $34162713446400$ by $362880$ .

$94143280$