Question

The geographical distribution of hometown of some 80 students at DLSU-D is given as: 50 from Cavite, 10 from Laguna, and 20 from Manila. Suppose three students are selected. Find the probability that they all come from the three places.

Answer 1

The probability none comes from C. is (30/80)*(29/79)*(28/78)=0.0494.

The three buttons have to be pressed in a certain order. Because three buttons have all been pressed many times, then the buttons will be assumed to be distinct. 
The chances are then 3! or 6, and the probability is (1/6)
ABC

ACB
BCA
BAC
CAB
CBA 

In this instance, there are 10 ways to choose each button, three times, independent, since the buttons don't have to be distinct. This is 10^3 or 1000, and the probability is (1/1000).