Solve 12!/5!7!+12!/6!6!

$$\frac { 12 ! } { 5 ! 7 ! } + \frac { 12 ! } { 6 ! 6 ! }$$

Evaluate

$$1716$$

Solution Steps

Multiply 6! and 6! to get \left(6!\right)^{2}.

$$\frac{12!}{5!\times 7!}+\frac{12!}{\left(6!\right)^{2}}$$

The factorial of 12 is 479001600.

$$\frac{479001600}{5!\times 7!}+\frac{12!}{\left(6!\right)^{2}}$$

The factorial of 5 is 120.

$$\frac{479001600}{120\times 7!}+\frac{12!}{\left(6!\right)^{2}}$$

The factorial of 7 is 5040.

$$\frac{479001600}{120\times 5040}+\frac{12!}{\left(6!\right)^{2}}$$

Multiply 120 and 5040 to get 604800.

$$\frac{479001600}{604800}+\frac{12!}{\left(6!\right)^{2}}$$

Divide 479001600 by 604800 to get 792.

$$792+\frac{12!}{\left(6!\right)^{2}}$$

The factorial of 12 is 479001600.

$$792+\frac{479001600}{\left(6!\right)^{2}}$$

The factorial of 6 is 720.

$$792+\frac{479001600}{720^{2}}$$

Calculate 720 to the power of 2 and get 518400.

$$792+\frac{479001600}{518400}$$

Divide 479001600 by 518400 to get 924.

$$792+924$$

Add 792 and 924 to get 1716.

$$1716$$

Factor

$$2^{2}\times 3\times 11\times 13$$