Solve 10!+10!/1!+10!/2!+10!/3!

$$10 ! + \frac { 10 ! } { 1 ! } + \frac { 10 ! } { 2 ! } + \frac { 10 ! } { 3 ! }$$

Evaluate

$$9676800$$

Solution Steps

The factorial of 10 is 3628800.

$$3628800+\frac{10!}{1!}+\frac{10!}{2!}+\frac{10!}{3!}$$

The factorial of 10 is 3628800.

$$3628800+\frac{3628800}{1!}+\frac{10!}{2!}+\frac{10!}{3!}$$

The factorial of 1 is 1.

$$3628800+\frac{3628800}{1}+\frac{10!}{2!}+\frac{10!}{3!}$$

Anything divided by one gives itself.

$$3628800+3628800+\frac{10!}{2!}+\frac{10!}{3!}$$

Add 3628800 and 3628800 to get 7257600.

$$7257600+\frac{10!}{2!}+\frac{10!}{3!}$$

The factorial of 10 is 3628800.

$$7257600+\frac{3628800}{2!}+\frac{10!}{3!}$$

The factorial of 2 is 2.

$$7257600+\frac{3628800}{2}+\frac{10!}{3!}$$

Divide 3628800 by 2 to get 1814400.

$$7257600+1814400+\frac{10!}{3!}$$

Add 7257600 and 1814400 to get 9072000.

$$9072000+\frac{10!}{3!}$$

The factorial of 10 is 3628800.

$$9072000+\frac{3628800}{3!}$$

The factorial of 3 is 6.

$$9072000+\frac{3628800}{6}$$

Divide 3628800 by 6 to get 604800.

$$9072000+604800$$

Add 9072000 and 604800 to get 9676800.

$$9676800$$

Factor

$$2^{11}\times 3^{3}\times 5^{2}\times 7$$