Answer to Question #1736 in Statistics and Probability for Danah Cummins

Question

A committee of 3 people are selected from a grouping of 15 doctors and 12 dentists.
i. In how many ways can the 3 people be selected:if there are no restrictions
ii.If the selection must contain exactly two doctors
iii.If the selection must contain at least 1 doctor and at least 1 dentist

Answer 1

i. There are 4 ways to select 3 people: 3 doctors, 2 doctors 1 dentist,& 1 doctor 2 dentists,& 3 dentists.
ii. If the selection must contain exactly two doctors, there is only one way of selection: 2 doctors 1 dentist.
iii. If the selection must contain at least 1 doctor and at least 1 dentist, there are two ways:& 2 doctors 1 dentist,& 1 doctor 2 dentists.