Chapter 13.4, Problem 32SPR

To determine

To calculate:

Probability that Paige chooses $3$ particular books for checking out from $10$ initial books.

Answer to Problem 32SPR

Probability that Paige chooses $3$ particular books for checking out from $10$ initial books is $\frac{1}{20}$ .

Explanation of Solution

Given information:

Paige chooses $10$ books at library.

A person can choose $3$ books from $10$ books in $C{}_3=\frac{10!}{\left(10-3\right)!3!}$ ways.

The probability that the person chooses $3$ particular books is equal to the singular outcome of the three books divided by the total number $3$ books can be chosen from $10$ .

  $P$ (chooses $3$ particular books) ,

  $\begin{array}{l}=\frac{1}{C{}_3}\\ =\frac{\begin{array}{l}1\\ 10!\end{array}}{\left(10-3\right)!3!}\\ =\frac{1}{\begin{array}{l}10\times 9\times 8\\ 3\times 2\times 1\end{array}}\\ =\frac{1}{20}\end{array}$

Therefore, Probability of the given event is $\frac{1}{20}$ .