Solve 5!/2!*3!*(2/3)^2*(1/3)^3

$$\frac { 5 ! } { 2 ! \times 3 ! } \times ( \frac { 2 } { 3 } ) ^ { 2 } \times ( \frac { 1 } { 3 } ) ^ { 3 }$$

Evaluate

$$\frac{40}{243}\approx 0.164609053$$

Solution Steps

The factorial of 5 is 120.

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

The factorial of 2 is 2.

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

The factorial of 3 is 6.

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

Multiply 2 and 6 to get 12.

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

Divide 120 by 12 to get 10.

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

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

$$10\times \frac{4}{9}\times \left(\frac{1}{3}\right)^{3}$$

Express 10\times \frac{4}{9} as a single fraction.

$$\frac{10\times 4}{9}\times \left(\frac{1}{3}\right)^{3}$$

Multiply 10 and 4 to get 40.

$$\frac{40}{9}\times \left(\frac{1}{3}\right)^{3}$$

Calculate \frac{1}{3} to the power of 3 and get \frac{1}{27}.

$$\frac{40}{9}\times \frac{1}{27}$$

Multiply \frac{40}{9} times \frac{1}{27} by multiplying numerator times numerator and denominator times denominator.

$$\frac{40\times 1}{9\times 27}$$

Do the multiplications in the fraction \frac{40\times 1}{9\times 27}.

$$\frac{40}{243}$$

Factor

$$\frac{2 ^ {3} \cdot 5}{3 ^ {5}} = 0.1646090534979424$$