Solve 15!/12!3!0.7^120.3^3

$$\frac{ 15 ! }{ 12 ! 3 ! } { 0.7 }^{ 12 } { 0.3 }^{ 3 }$$

Evaluate

$$0.170040213264285$$

Solution Steps

The factorial of 15 is 1307674368000.

$$\frac{1307674368000}{12!\times 3!}\times 0.7^{12}\times 0.3^{3}$$

The factorial of 12 is 479001600.

$$\frac{1307674368000}{479001600\times 3!}\times 0.7^{12}\times 0.3^{3}$$

The factorial of 3 is 6.

$$\frac{1307674368000}{479001600\times 6}\times 0.7^{12}\times 0.3^{3}$$

Multiply 479001600 and 6 to get 2874009600.

$$\frac{1307674368000}{2874009600}\times 0.7^{12}\times 0.3^{3}$$

Divide 1307674368000 by 2874009600 to get 455.

$$455\times 0.7^{12}\times 0.3^{3}$$

Calculate 0.7 to the power of 12 and get 0.013841287201.

$$455\times 0.013841287201\times 0.3^{3}$$

Multiply 455 and 0.013841287201 to get 6.297785676455.

$$6.297785676455\times 0.3^{3}$$

Calculate 0.3 to the power of 3 and get 0.027.

$$6.297785676455\times 0.027$$

Multiply 6.297785676455 and 0.027 to get 0.170040213264285.

$$0.170040213264285$$

Factor

$$\frac{13 \cdot 3 ^ {3} \cdot 7 ^ {13}}{2 ^ {15} \cdot 5 ^ {14}} = 0.170040213264285$$