Finite Math Examples

20 C 4

${}_{20}C_{4}$

Step 1

Evaluate

20 C 4

${}_{20}C_{4}$ using the formula

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

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

\frac{20!}{(20 - 4)! 4!}

$\frac{20!}{(20 - 4)! 4!}$

Step 2

Subtract

4

$4$ from

20

$20$ .

\frac{20!}{(16)! 4!}

$\frac{20!}{(16)! 4!}$

Step 3

Simplify

\frac{20!}{(16)! 4!}

$\frac{20!}{(16)! 4!}$ .

Tap for more steps...

Step 3.1

Rewrite

20!

$20!$ as

20 \cdot 19 \cdot 18 \cdot 17 \cdot 16!

$20 \cdot 19 \cdot 18 \cdot 17 \cdot 16!$ .

\frac{20 \cdot 19 \cdot 18 \cdot 17 \cdot 16!}{(16)! 4!}

$\frac{20 \cdot 19 \cdot 18 \cdot 17 \cdot 16!}{(16)! 4!}$

Step 3.2

Cancel the common factor of

16!

$16!$ .

Tap for more steps...

Step 3.2.1

Cancel the common factor.

$\frac{20 \cdot 19 \cdot 18 \cdot 17 \cdot 16!}{(16)! 4!}$

Step 3.2.2

Rewrite the expression.

$\frac{20 \cdot 19 \cdot 18 \cdot 17}{4!}$

Step 3.3

Simplify the numerator.

Tap for more steps...

Step 3.3.1

Multiply

$20$ by

$19$ .

$\frac{380 \cdot 18 \cdot 17}{4!}$

Step 3.3.2

Multiply

$380$ by

$18$ .

$\frac{6840 \cdot 17}{4!}$

Step 3.3.3

Multiply

$6840$ by

$17$ .

$\frac{116280}{4!}$

Step 3.4

Simplify the denominator.

Tap for more steps...

Step 3.4.1

Expand

$4!$ to

$4 \cdot 3 \cdot 2 \cdot 1$ .

$\frac{116280}{4 \cdot 3 \cdot 2 \cdot 1}$

Step 3.4.2

Multiply

$4 \cdot 3 \cdot 2 \cdot 1$ .

Tap for more steps...

Step 3.4.2.1

Multiply

$4$ by

$3$ .

$\frac{116280}{12 \cdot 2 \cdot 1}$

Step 3.4.2.2

Multiply

$12$ by

$2$ .

$\frac{116280}{24 \cdot 1}$

Step 3.4.2.3

Multiply

$24$ by

$1$ .

$\frac{116280}{24}$

Step 3.5

Divide

$116280$ by

$24$ .

$4845$