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.

Step-by-step explanation:

Probability of event

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

and

`^nC_r=(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} =(^8C_3*^5C_2)/(^(13)C_5) \\ =(560)/(1287) \end{gathered}`

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