Chapter 13, Problem 33RE

(a)

To determine

To find:The number ways $18$ people have different birthday.

Answer to Problem 33RE

The number ways $18$ people have different birthday is $8.6346\times {10}^{45}$ .

Explanation of Solution

The number ways $18$ people have different birthdayis calculated as,

  $\begin{array}{c}\text{Number}=P\left(365,18\right)\\ =8.6346\times {10}^{45}\end{array}$

(b)

To determine

To find: The probability that $18$ people have different birthday.

Answer to Problem 33RE

The probability that $18$ people have different birthday is $0.6531$ .

Explanation of Solution

The probability that $18$ people have different birthday is calculated as,

  $\begin{array}{c}\text{Probability}=\frac{8.6346\times {10}^{45}}{{365}^{18}}\\ =0.6531\end{array}$

(c)

To determine

To find: The probability that $18$ people at least 2 have same birthday.

Answer to Problem 33RE

The probability that $18$ people at least 2 have same birthday is $0.6531$ .

Explanation of Solution

The probability that $18$ people at least 2 have same birthday is calculated as,

  $\begin{array}{c}\text{Probability}=1-\frac{8.6346\times {10}^{45}}{{365}^{18}}\\ =1-0.6531\\ =0.3469\end{array}$