Solve (5!/6-6!/4!(6-4)!)^3

$$( \frac { 5 ! } { 6 } - \frac { 6 ! } { 4 ! ( 6 - 4 ) ! } ) ^ { 3 }$$

Evaluate

$$125$$

Solution Steps

The factorial of 5 is 120.

$$\left(\frac{120}{6}-\frac{6!}{4!\left(6-4\right)!}\right)^{3}$$

Divide 120 by 6 to get 20.

$$\left(20-\frac{6!}{4!\left(6-4\right)!}\right)^{3}$$

The factorial of 6 is 720.

$$\left(20-\frac{720}{4!\left(6-4\right)!}\right)^{3}$$

The factorial of 4 is 24.

$$\left(20-\frac{720}{24\left(6-4\right)!}\right)^{3}$$

Subtract 4 from 6 to get 2.

$$\left(20-\frac{720}{24\times 2!}\right)^{3}$$

The factorial of 2 is 2.

$$\left(20-\frac{720}{24\times 2}\right)^{3}$$

Multiply 24 and 2 to get 48.

$$\left(20-\frac{720}{48}\right)^{3}$$

Divide 720 by 48 to get 15.

$$\left(20-15\right)^{3}$$

Subtract 15 from 20 to get 5.

$$5^{3}$$

Calculate 5 to the power of 3 and get 125.

$$125$$

Factor

$$5^{3}$$