Solve 12!/3!9!/frac{15!{3!12!}}

$$\frac { \frac { 12 ! } { 3 ! 9 ! } } { \frac { 15 ! } { 3 ! 12 ! } }$$

Evaluate

$$\frac{44}{91}\approx 0.483516484$$

Solution Steps

Divide \frac{12!}{3!\times 9!} by \frac{15!}{3!\times 12!} by multiplying \frac{12!}{3!\times 9!} by the reciprocal of \frac{15!}{3!\times 12!}.

$$\frac{12!\times 3!\times 12!}{3!\times 9!\times 15!}$$

Cancel out 3! in both numerator and denominator.

$$\frac{12!\times 12!}{9!\times 15!}$$

Multiply 12! and 12! to get \left(12!\right)^{2}.

$$\frac{\left(12!\right)^{2}}{9!\times 15!}$$

The factorial of 12 is 479001600.

$$\frac{479001600^{2}}{9!\times 15!}$$

Calculate 479001600 to the power of 2 and get 229442532802560000.

$$\frac{229442532802560000}{9!\times 15!}$$

The factorial of 9 is 362880.

$$\frac{229442532802560000}{362880\times 15!}$$

The factorial of 15 is 1307674368000.

$$\frac{229442532802560000}{362880\times 1307674368000}$$

Multiply 362880 and 1307674368000 to get 474528874659840000.

$$\frac{229442532802560000}{474528874659840000}$$

Reduce the fraction \frac{229442532802560000}{474528874659840000} to lowest terms by extracting and canceling out 5214603018240000.

$$\frac{44}{91}$$

Factor

$$\frac{2 ^ {2} \cdot 11}{7 \cdot 13} = 0.4835164835164835$$