How many different values are possible for the random variable Y?

Question

involving drawing calculators from a box of working and broken calculators. Assume that the box contains 14 calculators: 12 that work and 2 that do not work. A sample of 3 calculators is selected and a random variable Y is defined as the number of calculators selected which do not work.
How many different values are possible for the random variable Y?

Answer 1

If only 2 calculators don't work, then at most 2 can be selected that don't work.  So the only choices for Y are 0, 1, and 2 -- that's 3 different values.