Solve 7!/(7-5)!*5!*.43^5*.57^7*5

$$\frac { 7 ! } { ( 7 - 5 ) ! \cdot 5 ! } \cdot .43 ^ { 5 } \cdot .57 ^ { 7 \cdot 5 }$$

Evaluate

$$0.00000000088141720015777891326892053695459197469078401418866504355513898860866479$$

Solution Steps

The factorial of 7 is 5040.

$$\frac{5040}{\left(7-5\right)!\times 5!}\times 0.43^{5}\times 0.57^{7\times 5}$$

Subtract 5 from 7 to get 2.

$$\frac{5040}{2!\times 5!}\times 0.43^{5}\times 0.57^{7\times 5}$$

The factorial of 2 is 2.

$$\frac{5040}{2\times 5!}\times 0.43^{5}\times 0.57^{7\times 5}$$

The factorial of 5 is 120.

$$\frac{5040}{2\times 120}\times 0.43^{5}\times 0.57^{7\times 5}$$

Multiply 2 and 120 to get 240.

$$\frac{5040}{240}\times 0.43^{5}\times 0.57^{7\times 5}$$

Divide 5040 by 240 to get 21.

$$21\times 0.43^{5}\times 0.57^{7\times 5}$$

Calculate 0.43 to the power of 5 and get 0.0147008443.

$$21\times 0.0147008443\times 0.57^{7\times 5}$$

Multiply 21 and 0.0147008443 to get 0.3087177303.

$$0.3087177303\times 0.57^{7\times 5}$$

Multiply 7 and 5 to get 35.

$$0.3087177303\times 0.57^{35}$$

Calculate 0.57 to the power of 35 and get 0.0000000028550909573650066229089548892507907074710182727352898122649193.

$$0.3087177303\times 0.0000000028550909573650066229089548892507907074710182727352898122649193$$

Multiply 0.3087177303 and 0.0000000028550909573650066229089548892507907074710182727352898122649193 to get 0.00000000088141720015777891326892053695459197469078401418866504355513898860866479.

$$0.00000000088141720015777891326892053695459197469078401418866504355513898860866479$$

Factor

$$\frac{7 \cdot 3 ^ {36} \cdot 19 ^ {35} \cdot 43 ^ {5}}{2 ^ {80} \cdot 5 ^ {80}} = 8.814172001577791 \times 10^{-10}$$