Solution

All three the same: The only possibility here is three red balls and hence there is only one way of doing this.

Two the same, one different: There are two possibilities for two the same, red and blue. The third ball can then be chosen from any of the others, so there are three possibilities because we cannot choose the same colour again. Therefore the total number of ways is

All three different: Since there are four different colours of ball this is

Hence the number of different selections that can be made is

NOTE! Unlike the previous example, we added the combinations here as opposed to multiplying them.