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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?

 Jul 2, 2021
 #1
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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

 Jul 2, 2021
 #2
avatar+20 
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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. 

 Jul 2, 2021
edited by DrBrain824  Jul 2, 2021

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