Among the contestants in a competition are 42 women and 28 men. If 5 winners are randomly selected, what is the probability that they are all men?

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Answer 1 · 2017-02-27T08:11:15

#2340/288167 ~~ 0.00812#

If there are 42 women and 28 men, there are 70 contestants altogether.

Once one winner is chosen, there are 69 people left and so on ...

To have ALL men, the number of men to choose from will decrease, as will the total number.

#P(M,M,M,M,M) = 28/70 xx27/69xx26/68xx25/67xx24/66#

This multiplies to give a very uncomfortable fraction, even when simplified, so it is better either left as the calculation or as a decimal.

#(11,793,600)/(1,452,361,680) = 2340/288167#

#~~0.00812#

In simple terms, there is a very small chance of five men being chosen.