Solve 12!10!/14!9!

$$\frac { 12 ! 10 ! } { 14 ! 9 ! }$$

Evaluate

$$\frac{5}{91}\approx 0.054945055$$

Solution Steps

The factorial of 12 is 479001600.

$$\frac{479001600\times 10!}{14!\times 9!}$$

The factorial of 10 is 3628800.

$$\frac{479001600\times 3628800}{14!\times 9!}$$

Multiply 479001600 and 3628800 to get 1738201006080000.

$$\frac{1738201006080000}{14!\times 9!}$$

The factorial of 14 is 87178291200.

$$\frac{1738201006080000}{87178291200\times 9!}$$

The factorial of 9 is 362880.

$$\frac{1738201006080000}{87178291200\times 362880}$$

Multiply 87178291200 and 362880 to get 31635258310656000.

$$\frac{1738201006080000}{31635258310656000}$$

Reduce the fraction \frac{1738201006080000}{31635258310656000} to lowest terms by extracting and canceling out 347640201216000.

$$\frac{5}{91}$$

Factor

$$\frac{5}{7 \cdot 13} = 0.054945054945054944$$