Solve 33!/6!(33-6)!

$$\frac { 33 ! } { 6 ! ( 33 - 6 ) ! }$$

Evaluate

$$1107568$$

Solution Steps

The factorial of 33 is 8683317618811886495518194401280000000.

$$\frac{8683317618811886495518194401280000000}{6!\left(33-6\right)!}$$

The factorial of 6 is 720.

$$\frac{8683317618811886495518194401280000000}{720\left(33-6\right)!}$$

Subtract 6 from 33 to get 27.

$$\frac{8683317618811886495518194401280000000}{720\times 27!}$$

The factorial of 27 is 10888869450418352160768000000.

$$\frac{8683317618811886495518194401280000000}{720\times 10888869450418352160768000000}$$

Multiply 720 and 10888869450418352160768000000 to get 7839986004301213555752960000000.

$$\frac{8683317618811886495518194401280000000}{7839986004301213555752960000000}$$

Divide 8683317618811886495518194401280000000 by 7839986004301213555752960000000 to get 1107568.

$$1107568$$

Factor

$$2^{4}\times 7\times 11\times 29\times 31$$