Solve 10!*20/frac{4!{7!*4*4*3}}=

$$\frac { 10 ! \cdot 20 } { \frac { 4 ! } { 7 ! \cdot 4 \cdot 4 \cdot 3 } } =$$

Evaluate

$$731566080000$$

Solution Steps

The factorial of 10 is 3628800.

$$\frac{3628800\times 20}{\frac{4!}{7!\times 4\times 4\times 3}}$$

Multiply 3628800 and 20 to get 72576000.

$$\frac{72576000}{\frac{4!}{7!\times 4\times 4\times 3}}$$

The factorial of 4 is 24.

$$\frac{72576000}{\frac{24}{7!\times 4\times 4\times 3}}$$

The factorial of 7 is 5040.

$$\frac{72576000}{\frac{24}{5040\times 4\times 4\times 3}}$$

Multiply 5040 and 4 to get 20160.

$$\frac{72576000}{\frac{24}{20160\times 4\times 3}}$$

Multiply 20160 and 4 to get 80640.

$$\frac{72576000}{\frac{24}{80640\times 3}}$$

Multiply 80640 and 3 to get 241920.

$$\frac{72576000}{\frac{24}{241920}}$$

Reduce the fraction \frac{24}{241920} to lowest terms by extracting and canceling out 24.

$$\frac{72576000}{\frac{1}{10080}}$$

Divide 72576000 by \frac{1}{10080} by multiplying 72576000 by the reciprocal of \frac{1}{10080}.

$$72576000\times 10080$$

Multiply 72576000 and 10080 to get 731566080000.

$$731566080000$$

Factor

$$2^{15}\times 3^{6}\times 5^{4}\times 7^{2}$$