As men and women age, their risk of death increases. There are also health issues that can greatly impair older citizens' abilities to participate in activities and travel. Assume you are planning a 60th high school reunion and are wondering how many of the older adults would be able to attend. If you know that 22 women and 18 men are still alive, and are told that exactly 8 of them will attend, what is the probability that you would have exactly four men and exactly four women attend?

Question

Marley

Mathematics

29 September, 11:14

As men and women age, their risk of death increases. There are also health issues that can greatly impair older citizens' abilities to participate in activities and travel. Assume you are planning a 60th high school reunion and are wondering how many of the older adults would be able to attend. If you know that 22 women and 18 men are still alive, and are told that exactly 8 of them will attend, what is the probability that you would have exactly four men and exactly four women attend?

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Will Moran · Answer 1

The total number of men and women is 42.

So the number of ways of selecting 8 people from 42 is C (42,8) = 118030185.

The number of ways of selecting 4 men from 19 and 4 women from 23 is C (19,4) * C (23,4) = 3876*8855 = 34321980

Therefore, the required probability is 34321980 / 118030185 = 0.2907