Solve 15!/(15-3)!3!*left(.49right)^3*left(.51right)^12

$$\frac{ 15 ! }{ (15-3) ! 3 ! } \times { \left(.49 \right) }^{ 3 } \times { \left(.51 \right) }^{ 12 }$$

Evaluate

$$0.016574550145083605185439132295$$

Solution Steps

The factorial of 15 is 1307674368000.

$$\frac{1307674368000}{\left(15-3\right)!\times 3!}\times 0.49^{3}\times 0.51^{12}$$

Subtract 3 from 15 to get 12.

$$\frac{1307674368000}{12!\times 3!}\times 0.49^{3}\times 0.51^{12}$$

The factorial of 12 is 479001600.

$$\frac{1307674368000}{479001600\times 3!}\times 0.49^{3}\times 0.51^{12}$$

The factorial of 3 is 6.

$$\frac{1307674368000}{479001600\times 6}\times 0.49^{3}\times 0.51^{12}$$

Multiply 479001600 and 6 to get 2874009600.

$$\frac{1307674368000}{2874009600}\times 0.49^{3}\times 0.51^{12}$$

Divide 1307674368000 by 2874009600 to get 455.

$$455\times 0.49^{3}\times 0.51^{12}$$

Calculate 0.49 to the power of 3 and get 0.117649.

$$455\times 0.117649\times 0.51^{12}$$

Multiply 455 and 0.117649 to get 53.530295.

$$53.530295\times 0.51^{12}$$

Calculate 0.51 to the power of 12 and get 0.000309629344375621415601.

$$53.530295\times 0.000309629344375621415601$$

Multiply 53.530295 and 0.000309629344375621415601 to get 0.016574550145083605185439132295.

$$0.016574550145083605185439132295$$

Factor

$$\frac{13 \cdot 3 ^ {12} \cdot 7 ^ {7} \cdot 17 ^ {12}}{2 ^ {30} \cdot 5 ^ {29}} = 0.016574550145083605$$