An engagement team consists of a project manager, team leader, and four consultants. there are 2 candidates for the position of
project manager, 3 candidates for the position of team leader, and 7 candidates for the 4 consultant slots. if 2 out of 7 consultants refuse to be on the same team, how many different teams are possible?
I get C. If I see this on the test, id prolly get to 210 and then guess A B or C.
OK so for the first position we have only 2 possiblities ( proj manager) 3 for the team leader so and 7!/3!4! for the consultants
2*3*35 --> 210
Now I dunno how to figure out the constraints quickly but I eventually figured it out. Obvs. we want to figure out the total ways in which the two ARE on the same team.
I did it by AB are the two and XYZFN are the rest
ABXO (O stands for the other 4) So the first is ABXY, Z,F,N 4 possible choices
The next is
ABYO (but notice we already had YX so there are only 3 possible choices) ABZO ABFO ABNO No possible here we used them all up
