Permutation problems are very common on the Quantitative section of the GMAT. In order to do well, it is very important to understand how to solve these types of problems efficiently.
Luckily, there are two very easy methods that you can use to understand and quickly find a solution to these problems.
Let’s look at an example problem:
4 Couples wish to stand in a row for a group photo. How many arrangements of the 8 people are possible if each person must stand next to his or her partner.
(a) 324 (b) 352) (C) 384 (D) 426 (E) 512
It’s easiest to think of the four groups of couples as
C1 C2 C3 C4
Now how many different ways can we arrange these couples?
Since these couples are a factorial of 4 we simply multiply them out. 4 x 3 x 2 x 1.
And we are left with 24 permutations of the couples.
But we are not done yet! We still have to arrange the couples and each couple has the option of deciding who will stand on the right side. Since each couple has two ways to make this decision we can understand that as:
24 x 2 x 2 x 2 x 2 = 384 possible arrangements!
You’ve just solved this problem one way. But there is another, which you may or may not prefer.
Consider that we have 8 positions.
_ _ _ _ _ _ _ _
How many people can stand in the left position if there are 8 positions? Anyone!
8 _ _ _ _ _ _ _
So there are 8 possible options for the left position
But since only that person’s partner can stand next to him or her, there is only 1 possible option for the next position.
8 1 _ _ _ _ _ _
Now there will only be 6 possible people left for the next position.
8 1 6 _ _ _ _ _
Again, this person’s partner can only stand next to him or her, so once again there is only 1 possibility for this option.
8 1 6 1 _ _ _ _
Now there are only 4 people left.
8 1 6 1 4 1 _ _
We’re down to the last two people, which gives us only 2 options for this next position…and only one person remaining for the last option!
8 1 6 1 4 1 2 1
Now to arrive at the final answer, simply multiply these out.
This will be 8x6x4x2 = 384
It is important to understand both ways of doing permutations in order to succeed at the various problems one will face on the GMAT.
If you’re having trouble with Permutations, Manhattan Elite Prep can help. We have excellent GMAT instructors who are ready to assist you today!