Solve 8!/5!+9!/6!-5!/3!

$$\frac { 8 ! } { 5 ! } + \frac { 9 ! } { 6 ! } - \frac { 5 ! } { 3 ! }$$

Evaluate

$$820$$

Solution Steps

The factorial of 8 is 40320.

$$\frac{40320}{5!}+\frac{9!}{6!}-\frac{5!}{3!}$$

The factorial of 5 is 120.

$$\frac{40320}{120}+\frac{9!}{6!}-\frac{5!}{3!}$$

Divide 40320 by 120 to get 336.

$$336+\frac{9!}{6!}-\frac{5!}{3!}$$

The factorial of 9 is 362880.

$$336+\frac{362880}{6!}-\frac{5!}{3!}$$

The factorial of 6 is 720.

$$336+\frac{362880}{720}-\frac{5!}{3!}$$

Divide 362880 by 720 to get 504.

$$336+504-\frac{5!}{3!}$$

Add 336 and 504 to get 840.

$$840-\frac{5!}{3!}$$

The factorial of 5 is 120.

$$840-\frac{120}{3!}$$

The factorial of 3 is 6.

$$840-\frac{120}{6}$$

Divide 120 by 6 to get 20.

$$840-20$$

Subtract 20 from 840 to get 820.

$$820$$

Factor

$$2^{2}\times 5\times 41$$