Chapter 13.2, Problem 5CYU

To determine

To Find: The probability that all the four tickets is won by the girls.

Answer to Problem 5CYU

The required probability is $\frac{39}{783}$ .

Explanation of Solution

Given:

The number of boys is 15 and the number of girls is 15.

The number of movie tickets is 4.

Calculation:

Since, the total number of persons is 16 and the ticket is 4 then the simple events in the sample is,

  $n\left(S\right)=C\left(30,4\right)$

Consider that the four tickets were won by girls then the number of possible events is,

  $n\left(E\right)=C\left(15,4\right)$

Thus, the required probability of the event is obtained as,

  $\begin{array}{c}P\left(E\right)=\frac{n\left(E\right)}{n\left(S\right)}\\ =\frac{C\left(15,4\right)}{C\left(30,4\right)}\\ =\frac{15!}{\left(15-4\right)!4!}\cdot \frac{4!\left(30-4\right)!}{30!}\\ =\frac{39}{783}\end{array}$

Thus, the required probability is $\frac{39}{783}$ .