So you have 12 players paul can play all 3 positions, 5 can only play center or

forward and 6 can only play guard. How many basketball lineups can be made? (there are 1 center 2 guards and 2 forwards and the order of guards and forwards doesn't matter)

we have c1,f1,f2,g1,g2 are the positions I broke it into cases paul

playing c1,f1... No position and then use addition rule to get all lineups

So paul plays c1 = (1*5*4*6*5)/(2*2) I divided by 4 since the order of

the forwards and guards doesn't matter

Paul plays f1= ( 5*1*4*6*5)/2 I

divided by 2 since now the forward position is fixed but still the guard

position doesn't matter

And the others follow same idea is this correct? Thank you