Solve 5!/1!+5!/2!/frac{20!{5!*15!}}

$$\frac{ \frac{ 5 ! }{ 1 ! } + \frac{ 5 ! }{ 2 ! } }{ \frac{ 20 ! }{ 5 ! \times 15 ! } }$$

Evaluate

$$\frac{15}{1292}\approx 0.011609907$$

Solution Steps

The factorial of 5 is 120.

$$\frac{\frac{120}{1!}+\frac{5!}{2!}}{\frac{20!}{5!\times 15!}}$$

The factorial of 1 is 1.

$$\frac{\frac{120}{1}+\frac{5!}{2!}}{\frac{20!}{5!\times 15!}}$$

Anything divided by one gives itself.

$$\frac{120+\frac{5!}{2!}}{\frac{20!}{5!\times 15!}}$$

The factorial of 5 is 120.

$$\frac{120+\frac{120}{2!}}{\frac{20!}{5!\times 15!}}$$

The factorial of 2 is 2.

$$\frac{120+\frac{120}{2}}{\frac{20!}{5!\times 15!}}$$

Divide 120 by 2 to get 60.

$$\frac{120+60}{\frac{20!}{5!\times 15!}}$$

Add 120 and 60 to get 180.

$$\frac{180}{\frac{20!}{5!\times 15!}}$$

The factorial of 20 is 2432902008176640000.

$$\frac{180}{\frac{2432902008176640000}{5!\times 15!}}$$

The factorial of 5 is 120.

$$\frac{180}{\frac{2432902008176640000}{120\times 15!}}$$

The factorial of 15 is 1307674368000.

$$\frac{180}{\frac{2432902008176640000}{120\times 1307674368000}}$$

Multiply 120 and 1307674368000 to get 156920924160000.

$$\frac{180}{\frac{2432902008176640000}{156920924160000}}$$

Divide 2432902008176640000 by 156920924160000 to get 15504.

$$\frac{180}{15504}$$

Reduce the fraction \frac{180}{15504} to lowest terms by extracting and canceling out 12.

$$\frac{15}{1292}$$

Factor

$$\frac{3 \cdot 5}{2 ^ {2} \cdot 17 \cdot 19} = 0.011609907120743035$$