Chapter 10.5, Problem 78E

To determine

To calculate:

Probability that one chosen in science class is selected to work in the group.

Answer to Problem 78E

Probability that one chosen in science class is selected to work in the group is $0.002$ .

Explanation of Solution

Given information:

Total number students in class $=30$

Calculation:

Number of possible outcomes as the number of combinations of $30$ student taken $5$ at a time, $C{}_5$ because the order is not important.

Need to apply combinations,

The expression for combination for $n$ objects taken $r$ at a time is given by,

  $C{}_r=\frac{n!}{\left(n-r\right)!.r!}$

The required number of combinations are given as,

  $\begin{array}{l}C{}_5=\frac{30!}{\left(30-5\right)!.5!}\\ C{}_r=\frac{\mathrm{30.29.28.27.26.25}}{25!\mathrm{.5.4.3.2.1}}\\ C{}_r=142506\end{array}$

To find the number of favorable outcomes, there are $C{}_2$ ways in which a person concerned and $2$ best friends in the science class are chosen to work in group.

To find the probability,

  $P$ (person concerned and $2$ of her best friends work in group+,

  $\begin{array}{l}=\frac{C{}_2}{142506}\\ =\frac{351}{142506}\\ =0.002\end{array}$

Hence, answer is $0.002$ .