Source: Official Guide Revised GRE 1st Ed. Part 6; Set 3; #7

6

# A manager is forming a 6-person team

A manager is forming a 6-person team to work on a certain project. From the 11 candidates available for the team, the manager has already chosen 3 to be on the team. In selecting the other 3 team members, how many different combinations of 3 of the remaining candidates does the manager have to choose from? 6, 24, 56, 120, 462

### 3 Explanations

1

Jessica Gonzalez

We can also use Pascal's triangle to figure this one out!
:)

Mar 16, 2019 • Comment

Sam Kinsman

Yes, that's right! Good job spotting that :D
On the GRE, the fastest way to get to the answer is probably to use combinations :)

Miguel Reyes

Would you mind showing how to use Pascal's triangle in solving this please?

We are here calculating 8C3. This is the 3rd number on the 8th line of Pascal's Triangle (and remember, we start counting at 0, not 1). You'd have to create Pascal's Triangle, which isn't super quick. But the 8th row is this:
1, 8, 28, 56, 70, 56, 28, 8, 1
The third number (again, we start counting at 0) is 56. So that's our answer.
Hope that helps!

1

Sarah Beaulieu

Why does the 3 factorial cancel out the 6 factorial on top? I followed you all the way up until the end.

Sep 22, 2017 • Comment

Sam Kinsman

Happy to help! We have (8*7*6) / (3!). Notice that on top, we don't have 6!, it is just 8*7*6. Now, 3! = 3*2*1 = 6. So we have:

(8*7*6) / (3!) = (8*7*6) / 6

Here we can cancel the two sixes, and we are left with 8*7 = 56

2

Chris Lele

Oct 7, 2012 • Comment