Question

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Answer 1

Given:

There are 8 woman and 5 men with a chance to be on a game show.

The producer of the show is going to choose 5 of these people at random to be contestant.

To find:

What is the probability that the producer chooses 3 woman and 2 men.

Explanation:

Probability of event

$=\frac{Favorable\text{ cases}}{Total\text{ number of cases}}$

and

$^nC_r=\frac{n!}{(n-r)!r!}$

Solution:

First, we will find total number of contestant 8 + 5 = 13

Now, Probability of chooses 3 woman and 2 men

$\begin{gathered} =\frac{^8C_3\times^5C_2}{^{13}C_5} \\ =\frac{560}{1287} \end{gathered}$

Hence, this is the required probability of choosing 3 woman and 2 men.