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From a group of graduate students including 24 men and 22 women, 37 are chosen to participate in an archaeological dig.What is the probability that exactly 17 men and 20 women are chosen?

From a group of graduate students including 24 men and 22 women, 37 are chosen to-example-1
User JVene
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1 Answer

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Teerip, this is the solution:

Let's recall that Probability is the division between the total number of desired outcomes and the total number of outcomes.

We will use the Combinations formula to calculate the probability of women and men are selected because the order isn't important, as follows:

The group of men has 24 persons and we're looking to select 17.

The group of women has 22 individuals and we're looking to select 20.

Therefore, the total number of desired outcomes is:

• C (24, 17) = 24!/ 17! * 7! = 346,104

,

• C (22, 20) = 22!/ 20! * 2! = 231

,

• Total number of desired outcomes = 346,104 * 231 = 79'950,024

And the total number of outcomes is:

17 men + 20 women, out of 46 students. In consequence,

C (46, 37) = 46!/ 37

User CtrlX
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