Solve 7!/(7-3)!7!*.33^7*.67^7-3

$$\frac { 7 ! } { ( 7 - 3 ) ! 7 ! } \times .33 ^ { 7 } \times .67 ^ { 7 - 3 }$$

Evaluate

$$0.0000035783725052546967375$$

Solution Steps

The factorial of 7 is 5040.

$$\frac{5040}{\left(7-3\right)!\times 7!}\times 0.33^{7}\times 0.67^{7-3}$$

Subtract 3 from 7 to get 4.

$$\frac{5040}{4!\times 7!}\times 0.33^{7}\times 0.67^{7-3}$$

The factorial of 4 is 24.

$$\frac{5040}{24\times 7!}\times 0.33^{7}\times 0.67^{7-3}$$

The factorial of 7 is 5040.

$$\frac{5040}{24\times 5040}\times 0.33^{7}\times 0.67^{7-3}$$

Multiply 24 and 5040 to get 120960.

$$\frac{5040}{120960}\times 0.33^{7}\times 0.67^{7-3}$$

Reduce the fraction \frac{5040}{120960} to lowest terms by extracting and canceling out 5040.

$$\frac{1}{24}\times 0.33^{7}\times 0.67^{7-3}$$

Calculate 0.33 to the power of 7 and get 0.00042618442977.

$$\frac{1}{24}\times 0.00042618442977\times 0.67^{7-3}$$

Multiply \frac{1}{24} and 0.00042618442977 to get \frac{14206147659}{800000000000000}.

$$\frac{14206147659}{800000000000000}\times 0.67^{7-3}$$

Subtract 3 from 7 to get 4.

$$\frac{14206147659}{800000000000000}\times 0.67^{4}$$

Calculate 0.67 to the power of 4 and get 0.20151121.

$$\frac{14206147659}{800000000000000}\times 0.20151121$$

Multiply \frac{14206147659}{800000000000000} and 0.20151121 to get \frac{286269800420375739}{80000000000000000000000}.

$$\frac{286269800420375739}{80000000000000000000000}$$

Factor

$$\frac{3 ^ {6} \cdot 11 ^ {7} \cdot 67 ^ {4}}{2 ^ {25} \cdot 5 ^ {22}} = 3.578372505254697 \times 10^{-6}$$