What is the probability to have exactly 3 women? How do you do this? ( Statistics/Probability question)

Question

The answer is 0.397, but I don't get how.

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Answer 1 · 2018-02-16T07:03:37

Please see below.

We can select #5# from a class of #20# in

#C_5^20=(20xx19xx18xx17xx16)/(1xx2xx3xx4xx5)=15504# ways

then out of #12# women, #3# women can be selected in

#C_3^12=(12xx11xx10)/(1xx2xx3)=220# ways

and we can select #2# men from remaining #8# in

#C_2^8=(8xx7)/(1xx2)=28# ways

i.e. our selection of #3# women out of a sample of #5# could be in #220xx28# ways

Hence probability is #(220xx28)/15504~=0.397#