soumyadeeppaul1 wrote:
How can we use the FCP process to calculate this?
IMO, it can be something like this:
Total possible group - group with no senior partner
10*9*8 - 6*5*4 = 600, which is wrong.
But I don't understand why. Can someone please explain?
Hi soumyadeeppaul1,
In a Permutation, the order 'matters.' For example, if you had 10 people in a race, and you wanted to know the total number of possible winners for 1st/2nd/3rd place, then there would be (10)(9)(8) = 720 possible outcomes (assuming that there were no 'ties' during the race).
You're trying to use that same logic here, but the prompt asks us for 'groups' (NOT 'arrangements'), so you're ending up with too many 'duplicate entries' - and those duplicates are impacting your calculations.
Here's a simple example: if there were 3 people, then how many 'groups of 3' are there vs. how many different ways can you arrange the 3 people:
Let's refer to the people as A, B and C.
-Since there are only 3 people, there is only 1 possible 'group of 3' (A, B and C in whatever order you choose).
-With 3 people, there are (3)(2)(1) = 6 different arrangements (ABC, ACB, BAC, BCA, CAB and CBA).
There's a reason why your calculation is 6 TIMES larger than the correct answer: in both (10)(9)(8) and (6)(5)(4), each group is counted 6 TIMES (which each group should only be counted ONCE).
GMAT assassins aren't born, they're made,
Rich