Finite Math Examples

$\frac{25!}{2! \cdot 6! \cdot 13! \cdot 4!}$

Step 1

Rewrite $25!$ as $25 \cdot 24 \cdot 23 \cdot 22 \cdot 21 \cdot 20 \cdot 19 \cdot 18 \cdot 17 \cdot 16 \cdot 15 \cdot 14 \cdot 13!$ .

$\frac{25 \cdot 24 \cdot 23 \cdot 22 \cdot 21 \cdot 20 \cdot 19 \cdot 18 \cdot 17 \cdot 16 \cdot 15 \cdot 14 \cdot 13!}{2! \cdot 6! \cdot 13! \cdot 4!}$

Step 2

Cancel the common factor of $13!$ .

Tap for more steps...

Step 2.1

Cancel the common factor.

$\frac{25 \cdot 24 \cdot 23 \cdot 22 \cdot 21 \cdot 20 \cdot 19 \cdot 18 \cdot 17 \cdot 16 \cdot 15 \cdot 14 \cdot 13!}{2! \cdot 6! \cdot 13! \cdot 4!}$

Step 2.2

Rewrite the expression.

$\frac{25 \cdot 24 \cdot 23 \cdot 22 \cdot 21 \cdot 20 \cdot 19 \cdot 18 \cdot 17 \cdot 16 \cdot 15 \cdot 14}{2! \cdot 6! \cdot 4!}$

Step 3

Simplify the numerator.

Tap for more steps...

Step 3.1

Multiply $25$ by $24$ .

$\frac{600 \cdot 23 \cdot 22 \cdot 21 \cdot 20 \cdot 19 \cdot 18 \cdot 17 \cdot 16 \cdot 15 \cdot 14}{2! \cdot 6! \cdot 4!}$

Step 3.2

Multiply $600$ by $23$ .

$\frac{13800 \cdot 22 \cdot 21 \cdot 20 \cdot 19 \cdot 18 \cdot 17 \cdot 16 \cdot 15 \cdot 14}{2! \cdot 6! \cdot 4!}$

Step 3.3

Multiply $13800$ by $22$ .

$\frac{303600 \cdot 21 \cdot 20 \cdot 19 \cdot 18 \cdot 17 \cdot 16 \cdot 15 \cdot 14}{2! \cdot 6! \cdot 4!}$

Step 3.4

Multiply $303600$ by $21$ .

$\frac{6375600 \cdot 20 \cdot 19 \cdot 18 \cdot 17 \cdot 16 \cdot 15 \cdot 14}{2! \cdot 6! \cdot 4!}$

Step 3.5

Multiply $6375600$ by $20$ .

$\frac{127512000 \cdot 19 \cdot 18 \cdot 17 \cdot 16 \cdot 15 \cdot 14}{2! \cdot 6! \cdot 4!}$

Step 3.6

Multiply $127512000$ by $19$ .

$\frac{2422728000 \cdot 18 \cdot 17 \cdot 16 \cdot 15 \cdot 14}{2! \cdot 6! \cdot 4!}$

Step 3.7

Multiply $2422728000$ by $18$ .

$\frac{43609104000 \cdot 17 \cdot 16 \cdot 15 \cdot 14}{2! \cdot 6! \cdot 4!}$

Step 3.8

Multiply $43609104000$ by $17$ .

$\frac{741354768000 \cdot 16 \cdot 15 \cdot 14}{2! \cdot 6! \cdot 4!}$

Step 3.9

Multiply $741354768000$ by $16$ .

$\frac{11861676288000 \cdot 15 \cdot 14}{2! \cdot 6! \cdot 4!}$

Step 3.10

Multiply $11861676288000$ by $15$ .

$\frac{177925144320000 \cdot 14}{2! \cdot 6! \cdot 4!}$

Step 3.11

Multiply $177925144320000$ by $14$ .

$\frac{2490952020480000}{2! \cdot 6! \cdot 4!}$

Step 4

Simplify the denominator.

Tap for more steps...

Step 4.1

Expand $2!$ to $2 \cdot 1$ .

$\frac{2490952020480000}{2 \cdot 1 \cdot 6! 4!}$

Step 4.2

Multiply $2$ by $1$ .

$\frac{2490952020480000}{2 \cdot 6! 4!}$

Step 4.3

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

$\frac{2490952020480000}{2 \cdot (6 \cdot 5 \cdot 4 \cdot 3 \cdot 2 \cdot 1) 4!}$

Step 4.4

Multiply $6 \cdot 5 \cdot 4 \cdot 3 \cdot 2 \cdot 1$ .

Tap for more steps...

Step 4.4.1

Multiply $6$ by $5$ .

$\frac{2490952020480000}{2 \cdot (30 \cdot 4 \cdot 3 \cdot 2 \cdot 1) 4!}$

Step 4.4.2

Multiply $30$ by $4$ .

$\frac{2490952020480000}{2 \cdot (120 \cdot 3 \cdot 2 \cdot 1) 4!}$

Step 4.4.3

Multiply $120$ by $3$ .

$\frac{2490952020480000}{2 \cdot (360 \cdot 2 \cdot 1) 4!}$

Step 4.4.4

Multiply $360$ by $2$ .

$\frac{2490952020480000}{2 \cdot (720 \cdot 1) 4!}$

Step 4.4.5

Multiply $720$ by $1$ .

$\frac{2490952020480000}{2 \cdot 7204!}$

Step 4.5

Expand $4!$ to $4 \cdot 3 \cdot 2 \cdot 1$ .

$\frac{2490952020480000}{2 \cdot 720 (4 \cdot 3 \cdot 2 \cdot 1)}$

Step 4.6

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

Tap for more steps...

Step 4.6.1

Multiply $4$ by $3$ .

$\frac{2490952020480000}{2 \cdot 720 (12 \cdot 2 \cdot 1)}$

Step 4.6.2

Multiply $12$ by $2$ .

$\frac{2490952020480000}{2 \cdot 720 (24 \cdot 1)}$

Step 4.6.3

Multiply $24$ by $1$ .

$\frac{2490952020480000}{2 \cdot 720 \cdot 24}$

Step 4.7

Combine exponents.

Tap for more steps...

Step 4.7.1

Multiply $2$ by $720$ .

$\frac{2490952020480000}{1440 \cdot 24}$

Step 4.7.2

Multiply $1440$ by $24$ .

$\frac{2490952020480000}{34560}$

Step 5

Divide $2490952020480000$ by $34560$ .

$72076158000$