Hey Ron..Help me with the SLOT method on this one.

[dddanny2006]

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?

a.25
b.35
c.150
d.210
e.300

Source-Manhattan
Im getting my slot method wrong.Please help me.

Thanks

[jlucero]

First, recognize that you need to solve for project manager (PM), team leader (TL), and consultants (C) separately:

PM: one slot, two people = 2

TL: one slot, three people = 3

C: four slots, seven people = 7 * 6 * 5 * 4. With the slot method, you need to then stop and realize that there are 4! ways to rearrange the four people you have chosen. So you need to divide 840 by 24 to get 35 unique teams that can be created. Finally, since 2 of the consultants can't work together, we need to remove these specific teams from the 35 possibilities. If these two people are selected, we have two slots remaining with five other people to fill those slots, so there are 5 * 4 = 20, different ways to select the two other people, divided by 2, because there are 2! ways to choose those two other people. This means there are 35 - 10 = 25 consultant teams that can be selected.

Overall: 2 * 3 * 25 = 150

[RonPurewal]

Hi,
Please post problems in the correct forum. If this problem is from MGMAT, then it belongs in either the MGMAT CAT folder (if it's from a CAT exam) or the MGMAT non-CAT folder (if it's from any other MGMAT source).

Thanks.