Solve 19!/4!15!div20!/5!15!

$$\frac { 19 ! } { 4 ! 15 ! } \div \frac { 20 ! } { 5 ! 15 ! }$$

Evaluate

$$\frac{1}{4}=0.25$$

Solution Steps

Divide \frac{19!}{4!\times 15!} by \frac{20!}{5!\times 15!} by multiplying \frac{19!}{4!\times 15!} by the reciprocal of \frac{20!}{5!\times 15!}.

$$\frac{19!\times 5!\times 15!}{4!\times 15!\times 20!}$$

Cancel out 15! in both numerator and denominator.

$$\frac{5!\times 19!}{4!\times 20!}$$

The factorial of 5 is 120.

$$\frac{120\times 19!}{4!\times 20!}$$

The factorial of 19 is 121645100408832000.

$$\frac{120\times 121645100408832000}{4!\times 20!}$$

Multiply 120 and 121645100408832000 to get 14597412049059840000.

$$\frac{14597412049059840000}{4!\times 20!}$$

The factorial of 4 is 24.

$$\frac{14597412049059840000}{24\times 20!}$$

The factorial of 20 is 2432902008176640000.

$$\frac{14597412049059840000}{24\times 2432902008176640000}$$

Multiply 24 and 2432902008176640000 to get 58389648196239360000.

$$\frac{14597412049059840000}{58389648196239360000}$$

Reduce the fraction \frac{14597412049059840000}{58389648196239360000} to lowest terms by extracting and canceling out 14597412049059840000.

$$\frac{1}{4}$$

Factor

$$\frac{1}{2 ^ {2}} = 0.25$$