Solve 15!/6!9!0.7^60.3^9

$$\frac{ 15 ! }{ 6 ! 9 ! } { 0.7 }^{ 6 } { 0.3 }^{ 9 }$$

Evaluate

$$0.011590004761335$$

Solution Steps

The factorial of 15 is 1307674368000.

$$\frac{1307674368000}{6!\times 9!}\times 0.7^{6}\times 0.3^{9}$$

The factorial of 6 is 720.

$$\frac{1307674368000}{720\times 9!}\times 0.7^{6}\times 0.3^{9}$$

The factorial of 9 is 362880.

$$\frac{1307674368000}{720\times 362880}\times 0.7^{6}\times 0.3^{9}$$

Multiply 720 and 362880 to get 261273600.

$$\frac{1307674368000}{261273600}\times 0.7^{6}\times 0.3^{9}$$

Divide 1307674368000 by 261273600 to get 5005.

$$5005\times 0.7^{6}\times 0.3^{9}$$

Calculate 0.7 to the power of 6 and get 0.117649.

$$5005\times 0.117649\times 0.3^{9}$$

Multiply 5005 and 0.117649 to get 588.833245.

$$588.833245\times 0.3^{9}$$

Calculate 0.3 to the power of 9 and get 0.000019683.

$$588.833245\times 0.000019683$$

Multiply 588.833245 and 0.000019683 to get 0.011590004761335.

$$0.011590004761335$$

Factor

$$\frac{11 \cdot 13 \cdot 3 ^ {9} \cdot 7 ^ {7}}{2 ^ {15} \cdot 5 ^ {14}} = 0.011590004761335$$