Chapter 11.9, Problem 9E

To determine

To calculate: the probability of chose all three girls.

Answer to Problem 9E

the probability of chose all three girls is $\frac{15}{202}$ .

Explanation of Solution

Given information :

Total boys = $8$

Total girls = $10$

Calculation:to find the probability to choose all three girls, first find the total possibilities of chose three students,

We have total $18$ students and we have to choose three students from them so use combination for this,

Total possibility = $\begin{array}{l}C{}_3\\ \frac{18!}{\begin{array}{l}3!\left(18-3\right)!\\ \frac{18·17·16·15!}{3·2·1·15!}\end{array}}\text{ [substitue n by 18 and r by 3 and subtract, expand factorial and divide out common factors] }\\ 816\text{ [multiply]}\end{array}$

Possibilities to choose three girls from ten girls, use the combination,

Possibilities = $\begin{array}{l}C{}_3\\ \frac{10!}{3!·\left(10-3\right)!}\text{ [substitue n by 10 and r by 3]}\\ \frac{10·9·8·7!}{3·2·1·7!}\text{ [subtract, expand fctorial and divide out common factors}]\\ 120\text{ [multiply]}\end{array}$

Now divide both the results,

Probability = $\begin{array}{l}\frac{120}{816}\\ \frac{15}{202}\end{array}$

Hence,the probability of chose all three girls is $\frac{15}{202}$ .