by RonPurewal Sat Aug 16, 2014 11:18 pm
MOST IMPORTANTLY
On official problems—
If you don't IMMEDIATELY know how to calculate the number of possibilities, JUST START MAKING A LIST.
On literally every GMAC combinatorics problem I've seen—excepting only the most basic ones (just straight products)—it has been quite feasible to just list out all of the possibilities.
For instance, if there are 8 teams in a league, you can very easily just list all the games:
Team 1 vs 2, 3, 4, 5, 6, 7, 8 (7 games)
Team 2 vs 3, 4, 5, 6, 7, 8 (6 more games)
Team 3 vs 4, 5, 6, 7, 8 (5 more)
Team 4 vs 5, 6, 7, 8 (4 more)
Team 5 vs 6, 7, 8 (3 more)
Team 6 vs 7, 8 (2 more)
Team 7 vs 8 (1 more)
7 + 6 + 5 + 4 + 3 + 2 + 1 = 28 games.
You should be able to make this list in 30 seconds or less. If you can't, then forget about the combinatorics formulas, and practice the lowly art of making lists.
One of the tragic aspects of the MGMAT CAT exams is that the numbers on combinatorics problems are, unfortunately, usually much bigger than the numbers in official problems.
The tragedy is that listing and counting possibilities—which just about ALWAYS works on official problems, as long as you don't dilly-dally too much before you get started—doesn't work nearly as often on the MGMAT problems. It becomes a tragedy if people decide, as a result, that trying to make a list "isn't worth it".
This is something that's in the queue of Things To Be Fixed/Things To Do. But there are a lot of other things in that queue.