Solve 12!/5!7!5^12-5*4^5

$$\frac{ 12 ! }{ 5 ! 7 ! } { 5 }^{ 12-5 } \times { 4 }^{ 5 }$$

Evaluate

$$63360000000$$

Solution Steps

The factorial of 12 is 479001600.

$$\frac{479001600}{5!\times 7!}\times 5^{12-5}\times 4^{5}$$

The factorial of 5 is 120.

$$\frac{479001600}{120\times 7!}\times 5^{12-5}\times 4^{5}$$

The factorial of 7 is 5040.

$$\frac{479001600}{120\times 5040}\times 5^{12-5}\times 4^{5}$$

Multiply 120 and 5040 to get 604800.

$$\frac{479001600}{604800}\times 5^{12-5}\times 4^{5}$$

Divide 479001600 by 604800 to get 792.

$$792\times 5^{12-5}\times 4^{5}$$

Subtract 5 from 12 to get 7.

$$792\times 5^{7}\times 4^{5}$$

Calculate 5 to the power of 7 and get 78125.

$$792\times 78125\times 4^{5}$$

Multiply 792 and 78125 to get 61875000.

$$61875000\times 4^{5}$$

Calculate 4 to the power of 5 and get 1024.

$$61875000\times 1024$$

Multiply 61875000 and 1024 to get 63360000000.

$$63360000000$$

Factor

$$2^{13}\times 3^{2}\times 5^{7}\times 11$$