The Screamers are coached by Coach Yellsalot. The Screamers have 12 players, but two of them, Bob and Yogi, refuse to play together. How many starting lineups

CPhil answered the question as    672    if Bob and Yogi are NOT together.

THEN, as a bonus,  he showed the answer IF Bob and Yogi could play on the same team

Thanx to BOTH of you !  

There are 3 different cases for the starting lineup.

Case 1: Bob starts (and Yogi doesn't). In this case, the coach must choose 4 more players from the 10 remaining players (remember that Yogi won't play, so there are only 10 players left to select from). Thus there are 10C2 lineups that the coach can choose.

Case 2: Yogi starts (and Bob doesn't). As in Case 1, the coach must choose 4 more players from the 10 remaining players. So there are 10C4 lineups in this case.

Case 3: Neither Bob nor Yogi starts. In this case, the coach must choose all 5 players in the lineup from the 10 remaining players. Hence there are 10C4 lineups in this case. To get the total number of starting lineups, we add the number of lineups in each of the cases:

Case 1 + Case 2 + Case 3 = 210 + 210 + 252 = 672

Bogus Solution:(This is what I did the first time)

Case 1(and 2): Bob is in the team but Yogi isn't. There are 11 people that can be on the team. 11 * 10 * 9 * 8 * 7 * 2(for Yogi's case). That is 110880.

Case 3: neither are on the team. 10 * 9 * 8 * 7 * 6 = 30240

Sum is 141120

Way off 

I get a little different answer from Ninja

Possible teams :

Team 1 : Bob is on the team and we can pick any 4 of the other 10 players [not counting Yogi ]  = C(10,4) = 210 possible teams

Team 2 :  Same as team 1 except that Yogi is on the team and we can pick any 4 of the other 10 players [not counting Bob ]  = C(10,4) = 210 possible teams

Team 3 :   Neither is on the team and we can pick any 5 of the other 10 players   = C(10,5) = 252 possible teams

So....the total teams, if the starting lineup can't contain both/either Bob and Yogi  = 2 * 210  + 252   = 672

Note.....the only remaining team is the one where both are on it and we can pick any 3 of the other 10 players  = C (10,3)   =  120

So all possible .teams = .....672  + 120  = 792   =  C(12,5)

@CPhill, you are wrong. Everything was correct up to this(From your post:)

Note.....the only remaining team is the one where both are on it and we can pick any 3 of the other 10 players  = C (10,3)   =  120

BUT...If you look at the question, it says that Bob and Yogi refuse to play together.

The Screamers are coached by Coach Yellsalot. The Screamers have 12 players, but two of them, Bob and Yogi, refuse to play together. How many starting lineups (of 5 players) can Coach Yellsalot make, if the starting lineup can't contain both Bob and Yogi? (The order of the 5 players in the lineup does not matter; that is, two lineups are the same if they consist of the same 5 players.)