Solve 10!/3!7!*(1/3)^10*(2/3)^3

$$\frac { 10 ! } { 3 ! 7 ! } \cdot ( \frac { 1 } { 3 } ) ^ { 10 } \cdot ( \frac { 2 } { 3 } ) ^ { 3 }$$

Evaluate

$$\frac{320}{531441}\approx 0.000602136$$

Solution Steps

The factorial of 10 is 3628800.

$$\frac{3628800}{3!\times 7!}\times \left(\frac{1}{3}\right)^{10}\times \left(\frac{2}{3}\right)^{3}$$

The factorial of 3 is 6.

$$\frac{3628800}{6\times 7!}\times \left(\frac{1}{3}\right)^{10}\times \left(\frac{2}{3}\right)^{3}$$

The factorial of 7 is 5040.

$$\frac{3628800}{6\times 5040}\times \left(\frac{1}{3}\right)^{10}\times \left(\frac{2}{3}\right)^{3}$$

Multiply 6 and 5040 to get 30240.

$$\frac{3628800}{30240}\times \left(\frac{1}{3}\right)^{10}\times \left(\frac{2}{3}\right)^{3}$$

Divide 3628800 by 30240 to get 120.

$$120\times \left(\frac{1}{3}\right)^{10}\times \left(\frac{2}{3}\right)^{3}$$

Calculate \frac{1}{3} to the power of 10 and get \frac{1}{59049}.

$$120\times \frac{1}{59049}\times \left(\frac{2}{3}\right)^{3}$$

Multiply 120 and \frac{1}{59049} to get \frac{120}{59049}.

$$\frac{120}{59049}\times \left(\frac{2}{3}\right)^{3}$$

Reduce the fraction \frac{120}{59049} to lowest terms by extracting and canceling out 3.

$$\frac{40}{19683}\times \left(\frac{2}{3}\right)^{3}$$

Calculate \frac{2}{3} to the power of 3 and get \frac{8}{27}.

$$\frac{40}{19683}\times \frac{8}{27}$$

Multiply \frac{40}{19683} times \frac{8}{27} by multiplying numerator times numerator and denominator times denominator.

$$\frac{40\times 8}{19683\times 27}$$

Do the multiplications in the fraction \frac{40\times 8}{19683\times 27}.

$$\frac{320}{531441}$$

Factor

$$\frac{2 ^ {6} \cdot 5}{3 ^ {12}} = 0.0006021364554108546$$