Solve 5!div4!div1!/10!div4!div6!

$$\frac{ 5 ! \div 4 ! \div 1 ! }{ 10 ! \div 4 ! \div 6 ! }$$

Evaluate

$$\frac{1}{42}\approx 0.023809524$$

Solution Steps

Divide \frac{\frac{5!}{4!}}{1!} by \frac{\frac{10!}{4!}}{6!} by multiplying \frac{\frac{5!}{4!}}{1!} by the reciprocal of \frac{\frac{10!}{4!}}{6!}.

$$\frac{\frac{5!}{4!}\times 6!}{1!\times \frac{10!}{4!}}$$

The factorial of 5 is 120.

$$\frac{\frac{120}{4!}\times 6!}{1!\times \frac{10!}{4!}}$$

The factorial of 4 is 24.

$$\frac{\frac{120}{24}\times 6!}{1!\times \frac{10!}{4!}}$$

Divide 120 by 24 to get 5.

$$\frac{5\times 6!}{1!\times \frac{10!}{4!}}$$

The factorial of 6 is 720.

$$\frac{5\times 720}{1!\times \frac{10!}{4!}}$$

Multiply 5 and 720 to get 3600.

$$\frac{3600}{1!\times \frac{10!}{4!}}$$

The factorial of 1 is 1.

$$\frac{3600}{1\times \frac{10!}{4!}}$$

The factorial of 10 is 3628800.

$$\frac{3600}{1\times \frac{3628800}{4!}}$$

The factorial of 4 is 24.

$$\frac{3600}{1\times \frac{3628800}{24}}$$

Divide 3628800 by 24 to get 151200.

$$\frac{3600}{1\times 151200}$$

Multiply 1 and 151200 to get 151200.

$$\frac{3600}{151200}$$

Reduce the fraction \frac{3600}{151200} to lowest terms by extracting and canceling out 3600.

$$\frac{1}{42}$$

Factor

$$\frac{1}{2 \cdot 3 \cdot 7} = 0.023809523809523808$$