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I have a hard time grasping the concept that half of the time F would be behind J. Can someone please explain this to me?
Hi,
maybe this will help:
take 2 objects, x and y. How many ways to arrange them?
Clearly, 2: xy and yx. Notice that in half the arrangements (1 out of 2) x is before y, and in the other half y is before x.
Take 3 objects, x, w, and y. There are 3! or 6 arrangements. In half (ie, 3) of those arrangements, x is before w, while in the other half w before x. Likewise, in half of the arrangements x is before y while in the other half y before x. And, also, in half the arrangements, w is before y while in the other half y before w.
Why would it be the case that Joey can be arranged ahead of Frankie more or less often than Frankie can be arranged ahead of Joey? Why not the other way around?
So, here, the easiest way to solve is certainly to take just half of the total arrangements: 6!/2 = 360, and choose D.
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Also, can this be down using straight combinations without getting the concept that half of the time F would be behind J?
Yes, it certainly can as the above poster demonstrated!
But many combinatorics questions on the GMAT resist pure formulaic treatment. A little bit of reasoning on these questions can save you an immense amount of time!