Solve 6!/4!(6-4)!/frac{6!{(6-3)!}}

$$\frac { \frac { 6 ! } { 4 ! ( 6 - 4 ) ! } } { \frac { 6 ! } { ( 6 - 3 ) ! } }$$

Evaluate

$$\frac{1}{8}=0.125$$

Solution Steps

Divide \frac{6!}{4!\left(6-4\right)!} by \frac{6!}{\left(6-3\right)!} by multiplying \frac{6!}{4!\left(6-4\right)!} by the reciprocal of \frac{6!}{\left(6-3\right)!}.

$$\frac{6!\left(6-3\right)!}{4!\left(6-4\right)!\times 6!}$$

Cancel out 6! in both numerator and denominator.

$$\frac{\left(6-3\right)!}{4!\left(6-4\right)!}$$

Subtract 3 from 6 to get 3.

$$\frac{3!}{4!\left(6-4\right)!}$$

The factorial of 3 is 6.

$$\frac{6}{4!\left(6-4\right)!}$$

The factorial of 4 is 24.

$$\frac{6}{24\left(6-4\right)!}$$

Subtract 4 from 6 to get 2.

$$\frac{6}{24\times 2!}$$

The factorial of 2 is 2.

$$\frac{6}{24\times 2}$$

Multiply 24 and 2 to get 48.

$$\frac{6}{48}$$

Reduce the fraction \frac{6}{48} to lowest terms by extracting and canceling out 6.

$$\frac{1}{8}$$

Factor

$$\frac{1}{2 ^ {3}} = 0.125$$