Solve 4!/3!div7!/5!*2!

$$\frac { 4 ! } { 3 ! } \div \frac { 7 ! } { 5 ! \times 2 ! }$$

Evaluate

$$\frac{4}{21}\approx 0.19047619$$

Solution Steps

Divide \frac{4!}{3!} by \frac{7!}{5!\times 2!} by multiplying \frac{4!}{3!} by the reciprocal of \frac{7!}{5!\times 2!}.

$$\frac{4!\times 5!\times 2!}{3!\times 7!}$$

The factorial of 4 is 24.

$$\frac{24\times 5!\times 2!}{3!\times 7!}$$

The factorial of 5 is 120.

$$\frac{24\times 120\times 2!}{3!\times 7!}$$

Multiply 24 and 120 to get 2880.

$$\frac{2880\times 2!}{3!\times 7!}$$

The factorial of 2 is 2.

$$\frac{2880\times 2}{3!\times 7!}$$

Multiply 2880 and 2 to get 5760.

$$\frac{5760}{3!\times 7!}$$

The factorial of 3 is 6.

$$\frac{5760}{6\times 7!}$$

The factorial of 7 is 5040.

$$\frac{5760}{6\times 5040}$$

Multiply 6 and 5040 to get 30240.

$$\frac{5760}{30240}$$

Reduce the fraction \frac{5760}{30240} to lowest terms by extracting and canceling out 1440.

$$\frac{4}{21}$$

Factor

$$\frac{2 ^ {2}}{3 \cdot 7} = 0.19047619047619047$$