Chapter 10.5, Problem 47E

To determine

To calculate:

The probability that you and your friend are chosen.

Answer to Problem 47E

The probability that you and your friend are chosen is $44850$ .

Explanation of Solution

Given information:

Total audience of people $=300$

Randomly selected people $=2$

Formula used:

Expression for combination

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

Where,

  $n=$ objects

  $r=$ time

Calculation:

The number of possible outcomes such as the number of combinations of $300$ people taken $2$ at a time, ${}_{300}{C}_2$ because the order is not important.

So, apply the expression for combination for $n$ objects taken $r$ at a time is as follows:

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

The required number of combinations are as follows:

  $\begin{array}{l}{}_{300}{C}_2=\frac{300!}{\left(300-2\right)!\cdot 2!}\\ =\frac{300!}{298!\cdot 2!}\\ =\frac{300\cdot 299\cdot 298!}{298!\cdot 2\cdot 1}\\ =44850\end{array}$

Hence, the probability that you and your friend are chosen $44850$ .