Solve (5!/8!*3!+12!/5!)

$$( \frac { 5 ! } { 8 ! } \times 3 ! + \frac { 12 ! } { 5 ! } )$$

Evaluate

$$\frac{223534081}{56}\approx 3991680.017857143$$

Solution Steps

The factorial of 5 is 120.

$$\frac{120}{8!}\times 3!+\frac{12!}{5!}$$

The factorial of 8 is 40320.

$$\frac{120}{40320}\times 3!+\frac{12!}{5!}$$

Reduce the fraction \frac{120}{40320} to lowest terms by extracting and canceling out 120.

$$\frac{1}{336}\times 3!+\frac{12!}{5!}$$

The factorial of 3 is 6.

$$\frac{1}{336}\times 6+\frac{12!}{5!}$$

Multiply \frac{1}{336} and 6 to get \frac{6}{336}.

$$\frac{6}{336}+\frac{12!}{5!}$$

Reduce the fraction \frac{6}{336} to lowest terms by extracting and canceling out 6.

$$\frac{1}{56}+\frac{12!}{5!}$$

The factorial of 12 is 479001600.

$$\frac{1}{56}+\frac{479001600}{5!}$$

The factorial of 5 is 120.

$$\frac{1}{56}+\frac{479001600}{120}$$

Divide 479001600 by 120 to get 3991680.

$$\frac{1}{56}+3991680$$

Convert 3991680 to fraction \frac{223534080}{56}.

$$\frac{1}{56}+\frac{223534080}{56}$$

Since \frac{1}{56} and \frac{223534080}{56} have the same denominator, add them by adding their numerators.

$$\frac{1+223534080}{56}$$

Add 1 and 223534080 to get 223534081.

$$\frac{223534081}{56}$$

Factor

$$\frac{43 \cdot 5198467}{2 ^ {3} \cdot 7} = 3991680\frac{1}{56} = 3991680.0178571427$$