Solve (0.565)(0.565-1)(0.565-2)(0.002)/3!+0.352(0.565-3)(0.001)/4!

$$\frac { ( 0.565 ) ( 0.565 - 1 ) ( 0.565 - 2 ) ( 0.002 ) } { 3 ! } + \frac { 0.352 ( 0.565 - 3 ) ( 0.001 ) } { 4 ! }$$

Evaluate

$$\frac{1964377}{24000000000}\approx 0.000081849$$

Solution Steps

Subtract 1 from 0.565 to get -0.435.

$$\frac{0.565\left(-0.435\right)\left(0.565-2\right)\times 0.002}{3!}+\frac{0.352\left(0.565-3\right)\times 0.001}{4!}$$

Multiply 0.565 and -0.435 to get -0.245775.

$$\frac{-0.245775\left(0.565-2\right)\times 0.002}{3!}+\frac{0.352\left(0.565-3\right)\times 0.001}{4!}$$

Subtract 2 from 0.565 to get -1.435.

$$\frac{-0.245775\left(-1.435\right)\times 0.002}{3!}+\frac{0.352\left(0.565-3\right)\times 0.001}{4!}$$

Multiply -0.245775 and -1.435 to get 0.352687125.

$$\frac{0.352687125\times 0.002}{3!}+\frac{0.352\left(0.565-3\right)\times 0.001}{4!}$$

Multiply 0.352687125 and 0.002 to get 0.00070537425.

$$\frac{0.00070537425}{3!}+\frac{0.352\left(0.565-3\right)\times 0.001}{4!}$$

The factorial of 3 is 6.

$$\frac{0.00070537425}{6}+\frac{0.352\left(0.565-3\right)\times 0.001}{4!}$$

Expand \frac{0.00070537425}{6} by multiplying both numerator and the denominator by 100000000000.

$$\frac{70537425}{600000000000}+\frac{0.352\left(0.565-3\right)\times 0.001}{4!}$$

Reduce the fraction \frac{70537425}{600000000000} to lowest terms by extracting and canceling out 75.

$$\frac{940499}{8000000000}+\frac{0.352\left(0.565-3\right)\times 0.001}{4!}$$

Subtract 3 from 0.565 to get -2.435.

$$\frac{940499}{8000000000}+\frac{0.352\left(-2.435\right)\times 0.001}{4!}$$

Multiply 0.352 and -2.435 to get -0.85712.

$$\frac{940499}{8000000000}+\frac{-0.85712\times 0.001}{4!}$$

Multiply -0.85712 and 0.001 to get -0.00085712.

$$\frac{940499}{8000000000}+\frac{-0.00085712}{4!}$$

The factorial of 4 is 24.

$$\frac{940499}{8000000000}+\frac{-0.00085712}{24}$$

Expand \frac{-0.00085712}{24} by multiplying both numerator and the denominator by 100000000.

$$\frac{940499}{8000000000}+\frac{-85712}{2400000000}$$

Reduce the fraction \frac{-85712}{2400000000} to lowest terms by extracting and canceling out 16.

$$\frac{940499}{8000000000}-\frac{5357}{150000000}$$

Least common multiple of 8000000000 and 150000000 is 24000000000. Convert \frac{940499}{8000000000} and \frac{5357}{150000000} to fractions with denominator 24000000000.

$$\frac{2821497}{24000000000}-\frac{857120}{24000000000}$$

Since \frac{2821497}{24000000000} and \frac{857120}{24000000000} have the same denominator, subtract them by subtracting their numerators.

$$\frac{2821497-857120}{24000000000}$$

Subtract 857120 from 2821497 to get 1964377.

$$\frac{1964377}{24000000000}$$

Factor

$$\frac{31 \cdot 63367}{3 \cdot 2 ^ {12} \cdot 5 ^ {9}} = 8.184904166666666 \times 10^{-5}$$