Solve 3!/12!*2!/11!*1!/10!

$$\frac { 3 ! } { 12 ! } \times \frac { 2 ! } { 11 ! } \times \frac { 1 ! } { 10 ! }$$

Evaluate

$$\frac{1}{5781951826624512000000}\approx 1.729519771 \cdot 10^{-22}$$

Solution Steps

The factorial of 3 is 6.

$$\frac{6}{12!}\times \frac{2!}{11!}\times \frac{1!}{10!}$$

The factorial of 12 is 479001600.

$$\frac{6}{479001600}\times \frac{2!}{11!}\times \frac{1!}{10!}$$

Reduce the fraction \frac{6}{479001600} to lowest terms by extracting and canceling out 6.

$$\frac{1}{79833600}\times \frac{2!}{11!}\times \frac{1!}{10!}$$

The factorial of 2 is 2.

$$\frac{1}{79833600}\times \frac{2}{11!}\times \frac{1!}{10!}$$

The factorial of 11 is 39916800.

$$\frac{1}{79833600}\times \frac{2}{39916800}\times \frac{1!}{10!}$$

Reduce the fraction \frac{2}{39916800} to lowest terms by extracting and canceling out 2.

$$\frac{1}{79833600}\times \frac{1}{19958400}\times \frac{1!}{10!}$$

Multiply \frac{1}{79833600} times \frac{1}{19958400} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1\times 1}{79833600\times 19958400}\times \frac{1!}{10!}$$

Do the multiplications in the fraction \frac{1\times 1}{79833600\times 19958400}.

$$\frac{1}{1593350922240000}\times \frac{1!}{10!}$$

The factorial of 1 is 1.

$$\frac{1}{1593350922240000}\times \frac{1}{10!}$$

The factorial of 10 is 3628800.

$$\frac{1}{1593350922240000}\times \frac{1}{3628800}$$

Multiply \frac{1}{1593350922240000} times \frac{1}{3628800} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1\times 1}{1593350922240000\times 3628800}$$

Do the multiplications in the fraction \frac{1\times 1}{1593350922240000\times 3628800}.

$$\frac{1}{5781951826624512000000}$$

Factor

$$\frac{1}{2 ^ {24} \cdot 3 ^ {12} \cdot 5 ^ {6} \cdot 7 ^ {3} \cdot 11 ^ {2}} = 1.7295197711527759 \times 10^{-22}$$