Solve 30!/1!29!(0.02)^1(1-0.02)^29

$$\frac { 30 ! } { 1 ! 29 ! } ( 0.02 ) ^ { 1 } ( 1 - 0.02 ) ^ { 29 }$$

Evaluate

$$0.33396999145863500899228451205205926383022433445998837628928$$

Solution Steps

The factorial of 30 is 265252859812191058636308480000000.

$$\frac{265252859812191058636308480000000}{1!\times 29!}\times 0.02^{1}\left(1-0.02\right)^{29}$$

The factorial of 1 is 1.

$$\frac{265252859812191058636308480000000}{1\times 29!}\times 0.02^{1}\left(1-0.02\right)^{29}$$

The factorial of 29 is 8841761993739701954543616000000.

$$\frac{265252859812191058636308480000000}{1\times 8841761993739701954543616000000}\times 0.02^{1}\left(1-0.02\right)^{29}$$

Multiply 1 and 8841761993739701954543616000000 to get 8841761993739701954543616000000.

$$\frac{265252859812191058636308480000000}{8841761993739701954543616000000}\times 0.02^{1}\left(1-0.02\right)^{29}$$

Divide 265252859812191058636308480000000 by 8841761993739701954543616000000 to get 30.

$$30\times 0.02^{1}\left(1-0.02\right)^{29}$$

Calculate 0.02 to the power of 1 and get 0.02.

$$30\times 0.02\left(1-0.02\right)^{29}$$

Multiply 30 and 0.02 to get 0.6.

$$0.6\left(1-0.02\right)^{29}$$

Subtract 0.02 from 1 to get 0.98.

$$0.6\times 0.98^{29}$$

Calculate 0.98 to the power of 29 and get 0.5566166524310583483204741867534321063837072240999806271488.

$$0.6\times 0.5566166524310583483204741867534321063837072240999806271488$$

Multiply 0.6 and 0.5566166524310583483204741867534321063837072240999806271488 to get 0.33396999145863500899228451205205926383022433445998837628928.

$$0.33396999145863500899228451205205926383022433445998837628928$$

Factor

$$\frac{3 \cdot 7 ^ {58}}{2 ^ {29} \cdot 5 ^ {59}} = 0.333969991458635$$