A room contains 15 professionals 4 doctors 2 nurses 5 person

A room contains 15 professionals: 4 doctors, 2 nurses, 5 personal trainers, 3 dentists, and 1 lawyer. You will select 4 of them to chair a committee.

what is the probability that the committee is entirely professionals of the same type?

what is the probability that the committee has at least 1 personal trainer?

what is the probability that all four members are from a different profession?

There are 15 professionals 4 doctors, 2 nurses, 5 trainers, 3 dentists and 1 lawyer

Selecting 4 from them can be done in 15C4 ways.

If all 4 are of the same type, no of ways of selecting is 4C4 or 5c4 because othres are less than 4.

Hence probability = favourable ways/total ways = 4c4+5c4/15c4

= 6/1365

2/455 =0.0044