Solve 8!7!/9!5!

$$\frac { 8 ! 7 ! } { 9 ! 5 ! }$$

Evaluate

$$\frac{14}{3}\approx 4.666666667$$

Solution Steps

The factorial of 8 is 40320.

$$\frac{40320\times 7!}{9!\times 5!}$$

The factorial of 7 is 5040.

$$\frac{40320\times 5040}{9!\times 5!}$$

Multiply 40320 and 5040 to get 203212800.

$$\frac{203212800}{9!\times 5!}$$

The factorial of 9 is 362880.

$$\frac{203212800}{362880\times 5!}$$

The factorial of 5 is 120.

$$\frac{203212800}{362880\times 120}$$

Multiply 362880 and 120 to get 43545600.

$$\frac{203212800}{43545600}$$

Reduce the fraction \frac{203212800}{43545600} to lowest terms by extracting and canceling out 14515200.

$$\frac{14}{3}$$

Factor

$$\frac{2 \cdot 7}{3} = 4\frac{2}{3} = 4.666666666666667$$