Solve 15!/10!5!0.7^100.3^5

$$\frac{ 15 ! }{ 10 ! 5 ! } { 0.7 }^{ 10 } { 0.3 }^{ 5 }$$

Evaluate

$$0.206130380977521$$

Solution Steps

The factorial of 15 is 1307674368000.

$$\frac{1307674368000}{10!\times 5!}\times 0.7^{10}\times 0.3^{5}$$

The factorial of 10 is 3628800.

$$\frac{1307674368000}{3628800\times 5!}\times 0.7^{10}\times 0.3^{5}$$

The factorial of 5 is 120.

$$\frac{1307674368000}{3628800\times 120}\times 0.7^{10}\times 0.3^{5}$$

Multiply 3628800 and 120 to get 435456000.

$$\frac{1307674368000}{435456000}\times 0.7^{10}\times 0.3^{5}$$

Divide 1307674368000 by 435456000 to get 3003.

$$3003\times 0.7^{10}\times 0.3^{5}$$

Calculate 0.7 to the power of 10 and get 0.0282475249.

$$3003\times 0.0282475249\times 0.3^{5}$$

Multiply 3003 and 0.0282475249 to get 84.8273172747.

$$84.8273172747\times 0.3^{5}$$

Calculate 0.3 to the power of 5 and get 0.00243.

$$84.8273172747\times 0.00243$$

Multiply 84.8273172747 and 0.00243 to get 0.206130380977521.

$$0.206130380977521$$

Factor

$$\frac{11 \cdot 13 \cdot 3 ^ {6} \cdot 7 ^ {11}}{2 ^ {15} \cdot 5 ^ {15}} = 0.206130380977521$$