Solve 10!/(10-9)!9!*left(.77right)^9*left(.23right)^10-9

$$\frac{ 10 ! }{ (10-9) ! 9 ! } \times { \left(.77 \right) }^{ 9 } \times { \left(.23 \right) }^{ 10-9 }$$

Evaluate

$$0.2188488972330943051$$

Solution Steps

The factorial of 10 is 3628800.

$$\frac{3628800}{\left(10-9\right)!\times 9!}\times 0.77^{9}\times 0.23^{10-9}$$

Subtract 9 from 10 to get 1.

$$\frac{3628800}{1!\times 9!}\times 0.77^{9}\times 0.23^{10-9}$$

The factorial of 1 is 1.

$$\frac{3628800}{1\times 9!}\times 0.77^{9}\times 0.23^{10-9}$$

The factorial of 9 is 362880.

$$\frac{3628800}{1\times 362880}\times 0.77^{9}\times 0.23^{10-9}$$

Multiply 1 and 362880 to get 362880.

$$\frac{3628800}{362880}\times 0.77^{9}\times 0.23^{10-9}$$

Divide 3628800 by 362880 to get 10.

$$10\times 0.77^{9}\times 0.23^{10-9}$$

Calculate 0.77 to the power of 9 and get 0.095151694449171437.

$$10\times 0.095151694449171437\times 0.23^{10-9}$$

Multiply 10 and 0.095151694449171437 to get 0.95151694449171437.

$$0.95151694449171437\times 0.23^{10-9}$$

Subtract 9 from 10 to get 1.

$$0.95151694449171437\times 0.23^{1}$$

Calculate 0.23 to the power of 1 and get 0.23.

$$0.95151694449171437\times 0.23$$

Multiply 0.95151694449171437 and 0.23 to get 0.2188488972330943051.

$$0.2188488972330943051$$

Factor

$$\frac{23 \cdot 7 ^ {9} \cdot 11 ^ {9}}{2 ^ {19} \cdot 5 ^ {19}} = 0.2188488972330943$$