Solve 3!/1!(3-1)!5!/4!(5-4)!

$$\frac{ 3 ! }{ 1 ! (3-1) ! } \frac{ 5 ! }{ 4 ! (5-4) ! }$$

Evaluate

$$15$$

Solution Steps

The factorial of 3 is 6.

$$\frac{6}{1!\left(3-1\right)!}\times \frac{5!}{4!\left(5-4\right)!}$$

The factorial of 1 is 1.

$$\frac{6}{1\left(3-1\right)!}\times \frac{5!}{4!\left(5-4\right)!}$$

Subtract 1 from 3 to get 2.

$$\frac{6}{1\times 2!}\times \frac{5!}{4!\left(5-4\right)!}$$

The factorial of 2 is 2.

$$\frac{6}{1\times 2}\times \frac{5!}{4!\left(5-4\right)!}$$

Multiply 1 and 2 to get 2.

$$\frac{6}{2}\times \frac{5!}{4!\left(5-4\right)!}$$

Divide 6 by 2 to get 3.

$$3\times \frac{5!}{4!\left(5-4\right)!}$$

The factorial of 5 is 120.

$$3\times \frac{120}{4!\left(5-4\right)!}$$

The factorial of 4 is 24.

$$3\times \frac{120}{24\left(5-4\right)!}$$

Subtract 4 from 5 to get 1.

$$3\times \frac{120}{24\times 1!}$$

The factorial of 1 is 1.

$$3\times \frac{120}{24\times 1}$$

Multiply 24 and 1 to get 24.

$$3\times \frac{120}{24}$$

Divide 120 by 24 to get 5.

$$3\times 5$$

Multiply 3 and 5 to get 15.

$$15$$

Factor

$$3\times 5$$