Solve (15!/13!)(0.7)^13(0.3)^2

$$( \frac { 15 ! } { 13 ! } ) ( 0.7 ) ^ { 13 } ( 0.3 ) ^ { 2 }$$

Evaluate

$$0.18312022966923$$

Solution Steps

The factorial of 15 is 1307674368000.

$$\frac{1307674368000}{13!}\times 0.7^{13}\times 0.3^{2}$$

The factorial of 13 is 6227020800.

$$\frac{1307674368000}{6227020800}\times 0.7^{13}\times 0.3^{2}$$

Divide 1307674368000 by 6227020800 to get 210.

$$210\times 0.7^{13}\times 0.3^{2}$$

Calculate 0.7 to the power of 13 and get 0.0096889010407.

$$210\times 0.0096889010407\times 0.3^{2}$$

Multiply 210 and 0.0096889010407 to get 2.034669218547.

$$2.034669218547\times 0.3^{2}$$

Calculate 0.3 to the power of 2 and get 0.09.

$$2.034669218547\times 0.09$$

Multiply 2.034669218547 and 0.09 to get 0.18312022966923.

$$0.18312022966923$$

Factor

$$\frac{3 ^ {3} \cdot 7 ^ {14}}{2 ^ {14} \cdot 5 ^ {14}} = 0.18312022966923$$