Solve =12!/(18-5)!5!=12!/7!5!=

$$= \frac { 12 ! } { ( 18 - 5 ) ! 5 ! } = \frac { 12 ! } { 7 ! 5 ! } =$$

Verify

Solution Steps

The factorial of 12 is 479001600.

$$\frac{479001600}{\left(18-5\right)!\times 5!}=\frac{12!}{7!\times 5!}$$

Subtract 5 from 18 to get 13.

$$\frac{479001600}{13!\times 5!}=\frac{12!}{7!\times 5!}$$

The factorial of 13 is 6227020800.

$$\frac{479001600}{6227020800\times 5!}=\frac{12!}{7!\times 5!}$$

The factorial of 5 is 120.

$$\frac{479001600}{6227020800\times 120}=\frac{12!}{7!\times 5!}$$

Multiply 6227020800 and 120 to get 747242496000.

$$\frac{479001600}{747242496000}=\frac{12!}{7!\times 5!}$$

Reduce the fraction \frac{479001600}{747242496000} to lowest terms by extracting and canceling out 479001600.

$$\frac{1}{1560}=\frac{12!}{7!\times 5!}$$

The factorial of 12 is 479001600.

$$\frac{1}{1560}=\frac{479001600}{7!\times 5!}$$

The factorial of 7 is 5040.

$$\frac{1}{1560}=\frac{479001600}{5040\times 5!}$$

The factorial of 5 is 120.

$$\frac{1}{1560}=\frac{479001600}{5040\times 120}$$

Multiply 5040 and 120 to get 604800.

$$\frac{1}{1560}=\frac{479001600}{604800}$$

Divide 479001600 by 604800 to get 792.

$$\frac{1}{1560}=792$$

Convert 792 to fraction \frac{1235520}{1560}.

$$\frac{1}{1560}=\frac{1235520}{1560}$$

Compare \frac{1}{1560} and \frac{1235520}{1560}.

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