Solve 15!/4!11!0.7^40.3^11

$$\frac{ 15 ! }{ 4 ! 11 ! } { 0.7 }^{ 4 } { 0.3 }^{ 11 }$$

Evaluate

$$0.000580575377655$$

Solution Steps

The factorial of 15 is 1307674368000.

$$\frac{1307674368000}{4!\times 11!}\times 0.7^{4}\times 0.3^{11}$$

The factorial of 4 is 24.

$$\frac{1307674368000}{24\times 11!}\times 0.7^{4}\times 0.3^{11}$$

The factorial of 11 is 39916800.

$$\frac{1307674368000}{24\times 39916800}\times 0.7^{4}\times 0.3^{11}$$

Multiply 24 and 39916800 to get 958003200.

$$\frac{1307674368000}{958003200}\times 0.7^{4}\times 0.3^{11}$$

Divide 1307674368000 by 958003200 to get 1365.

$$1365\times 0.7^{4}\times 0.3^{11}$$

Calculate 0.7 to the power of 4 and get 0.2401.

$$1365\times 0.2401\times 0.3^{11}$$

Multiply 1365 and 0.2401 to get 327.7365.

$$327.7365\times 0.3^{11}$$

Calculate 0.3 to the power of 11 and get 0.00000177147.

$$327.7365\times 0.00000177147$$

Multiply 327.7365 and 0.00000177147 to get 0.000580575377655.

$$0.000580575377655$$

Factor

$$\frac{13 \cdot 3 ^ {12} \cdot 7 ^ {5}}{2 ^ {15} \cdot 5 ^ {14}} = 0.000580575377655$$