Question 789037
let's say we have 100 doctors, then 37% of 100 gives us 37 doctors that are family practitioners
then we are told that at a gathering we have 5 doctors and to calculate the probability that 3  of them are family practitioners
now we use combinations to calculate the probability
we multiply the combination of 37 taken 3 at a time by the combination of 63 taken two at a time and then divide by the combination of 100 taken 5 at a time
the combination of 37 taken 3 at a time = 37! / (3! * (37-3)!) = 7770
the combination of 63 taken two at a time = 1953
the combination of 100 taken 5 at a time = 7.528752e7
now we can calculate
(7770 * 1953) / 7.528752e7
1.517481e7 / 7.528752e7
0.20155810684161199625
this tells us that the probability that 3 doctors are family practitioners is 20%