Solve (5000*100)/100!*e^-100

$$\frac { ( 5000 \cdot 100 ) } { 100 ! } \cdot e ^ { - 100 }$$

Evaluate

$$\frac{1}{186652430887888305363398477712533400981431936528763242937185927790435199986459831217882927952313036572507395841654447516502370421833728000000000000000000e^{100}}\approx 1.99304984 \cdot 10^{-196}$$

Solution Steps

Multiply 5000 and 100 to get 500000.

$$\frac{500000}{100!}e^{-100}$$

The factorial of 100 is 93326215443944152681699238856266700490715968264381621468592963895217599993229915608941463976156518286253697920827223758251185210916864000000000000000000000000.

$$\frac{500000}{93326215443944152681699238856266700490715968264381621468592963895217599993229915608941463976156518286253697920827223758251185210916864000000000000000000000000}e^{-100}$$

Reduce the fraction \frac{500000}{93326215443944152681699238856266700490715968264381621468592963895217599993229915608941463976156518286253697920827223758251185210916864000000000000000000000000} to lowest terms by extracting and canceling out 500000.

$$\frac{1}{186652430887888305363398477712533400981431936528763242937185927790435199986459831217882927952313036572507395841654447516502370421833728000000000000000000}e^{-100}$$