The following two questions seem similar to me, but according to the solutions, they are both solved in a different way.
Shouldn't they be solved in the same way? If so, which is the correct method?
How many 4-person committees are possible from a group of 9 people if, either John or Barbara (but not both) must be on the committee?
1C1 * 7C3 + 1C1 *7C3 = 70
A basketball team has 5 distinct positions. Out of 8 players, how many starting teams are possible if, the distinct positions are not taken into consideration, but either Mike or Ken (but not both) must start?
7C4 + 7C4 - 6C3 = 50
7C4: Number of starting combinations involving Mike or Ken
6C3: Number of starting combinations involving both Mike and Ken