A basketball team has ten players, three of which are all stars. How many five player starting lineups can be chosen that include at least two of the all stars?
+240 There are two cases,
1. Two all stars players and picked and there are 3 regular players
2. Three all star players are picked and there are 2 regular players
Let's start with case 1. There are 3c2 ways to pick the 2 all star players that will play, 3 ways. And there are 7c3 ways to pick the 3 regular players that play, 35 ways. 3*35 = 105, so 105 possible ways for case one.
For case 2, it is exactly the same logic, just different values. 3c3 = 1 way, and 7c2 = 21, 21*1 = 21.
21+105 = 126 ways i think
+20 First lets choose the stars on the court.
3 choose 2 = 3 * 2/2 * 1 = 3
Now, out of the 8 players left, 3 of them need to be on the court.
8 choose 3 = 8 * 7 * 6/6 = 56
56 * 3 = 168
There are 168 possibilities.
