Solve 5!/3!(5-3)!*{left(1/4right)}^3*{left(3/4right)}^2

$$\frac{ 5 ! }{ 3 ! (5-3) ! } \times { \left( \frac{ 1 }{ 4 } \right) }^{ 3 } \times { \left( \frac{ 3 }{ 4 } \right) }^{ 2 }$$

Evaluate

$$\frac{45}{512}=0.087890625$$

Solution Steps

The factorial of 5 is 120.

$$\frac{120}{3!\left(5-3\right)!}\times \left(\frac{1}{4}\right)^{3}\times \left(\frac{3}{4}\right)^{2}$$

The factorial of 3 is 6.

$$\frac{120}{6\left(5-3\right)!}\times \left(\frac{1}{4}\right)^{3}\times \left(\frac{3}{4}\right)^{2}$$

Subtract 3 from 5 to get 2.

$$\frac{120}{6\times 2!}\times \left(\frac{1}{4}\right)^{3}\times \left(\frac{3}{4}\right)^{2}$$

The factorial of 2 is 2.

$$\frac{120}{6\times 2}\times \left(\frac{1}{4}\right)^{3}\times \left(\frac{3}{4}\right)^{2}$$

Multiply 6 and 2 to get 12.

$$\frac{120}{12}\times \left(\frac{1}{4}\right)^{3}\times \left(\frac{3}{4}\right)^{2}$$

Divide 120 by 12 to get 10.

$$10\times \left(\frac{1}{4}\right)^{3}\times \left(\frac{3}{4}\right)^{2}$$

Calculate \frac{1}{4} to the power of 3 and get \frac{1}{64}.

$$10\times \frac{1}{64}\times \left(\frac{3}{4}\right)^{2}$$

Multiply 10 and \frac{1}{64} to get \frac{10}{64}.

$$\frac{10}{64}\times \left(\frac{3}{4}\right)^{2}$$

Reduce the fraction \frac{10}{64} to lowest terms by extracting and canceling out 2.

$$\frac{5}{32}\times \left(\frac{3}{4}\right)^{2}$$

Calculate \frac{3}{4} to the power of 2 and get \frac{9}{16}.

$$\frac{5}{32}\times \frac{9}{16}$$

Multiply \frac{5}{32} times \frac{9}{16} by multiplying numerator times numerator and denominator times denominator.

$$\frac{5\times 9}{32\times 16}$$

Do the multiplications in the fraction \frac{5\times 9}{32\times 16}.

$$\frac{45}{512}$$

Factor

$$\frac{3 ^ {2} \cdot 5}{2 ^ {9}} = 0.087890625$$