Solve 13!/4!(13-4)!211^4(1-211)^(13-4)

$$\frac { 13 ! } { 4 ! ( 13 - 4 ) ! } 211 ^ { 4 } ( 1 - 211 ) ^ { ( 13 - 4 ) }$$

Evaluate

$$-1125665914177508762073015000000000$$

Solution Steps

The factorial of 13 is 6227020800.

$$\frac{6227020800}{4!\left(13-4\right)!}\times 211^{4}\left(1-211\right)^{13-4}$$

The factorial of 4 is 24.

$$\frac{6227020800}{24\left(13-4\right)!}\times 211^{4}\left(1-211\right)^{13-4}$$

Subtract 4 from 13 to get 9.

$$\frac{6227020800}{24\times 9!}\times 211^{4}\left(1-211\right)^{13-4}$$

The factorial of 9 is 362880.

$$\frac{6227020800}{24\times 362880}\times 211^{4}\left(1-211\right)^{13-4}$$

Multiply 24 and 362880 to get 8709120.

$$\frac{6227020800}{8709120}\times 211^{4}\left(1-211\right)^{13-4}$$

Divide 6227020800 by 8709120 to get 715.

$$715\times 211^{4}\left(1-211\right)^{13-4}$$

Calculate 211 to the power of 4 and get 1982119441.

$$715\times 1982119441\left(1-211\right)^{13-4}$$

Multiply 715 and 1982119441 to get 1417215400315.

$$1417215400315\left(1-211\right)^{13-4}$$

Subtract 211 from 1 to get -210.

$$1417215400315\left(-210\right)^{13-4}$$

Subtract 4 from 13 to get 9.

$$1417215400315\left(-210\right)^{9}$$

Calculate -210 to the power of 9 and get -794280046581000000000.

$$1417215400315\left(-794280046581000000000\right)$$

Multiply 1417215400315 and -794280046581000000000 to get -1125665914177508762073015000000000.

$$-1125665914177508762073015000000000$$

Factor

$$-1125665914177508762073015000000000$$