sandipgumtya wrote:Is there any easier method to do?I really find this topic confusing.can u suggest something easier to remember and tackle all such type of prob.
Generally the permutations problems on the GMAT require one to go somewhat beyond the basic permutations rules in order to figure out the answer.
So, as is the case when one does this problem, often one can't just apply a simple formula or method that one has memorized and expect to get to the answer. Rather one has to go beyond that to analyzing the logic of the situation and figuring out how to apply a formula or general method in combination with some additional reasoning.
It's possible, Sandip, that the problems you are having with these types of questions stem from your understanding of how they work not being clear enough. If you don't really get how permutations work, then you will be rather challenged to figure out how to set things up to get the answer to a question like this one.
So my suggestion to you is to unconfuse yourself by really figuring out how permutations and combinations work.
Maybe this blog post I wrote will help.
https://infinitemindprep.com/permutation ... difficult/
Meanwhile, here is another way to answer this question. Maybe you will find this method easier to understand.
You can start by finding all the possible arrangements of the seven people around a circular table. That's pretty simple; it's just (7 - 1)! = 6! = 720.
We now have the maximum number of arrangements of 7 people around a circular table, and also we have a restriction. Because of that restriction the number of possible arrangements will be fewer than 720.
So already we can eliminate all the answer choices that are greater than 720, and we are down to A and B as possibilities.
Now we can get to the answer by subtracting from 720 all the arrangements where the two chiefs who won't sit together are sitting together.
Let's act as if the two of them sitting together were one unit.
If there were not an issue, the Chief of Naval Operations could sit to the right or the left of the Chief of the National Guard Bureau.
So there are two possible units composed of the two of them, Naval Operations Chief on the right and Naval Operation Chief on the left.
For each of those units there are five other chiefs.
So in a sense we have six units, the two of them, and the five others, and there are two different ways to arrange the two of them, so we have two sets of six units, each of which sets we can arrange around the table.
For each of those two sets there are (6 - 1)! = 5! = 120 different ways to arrange them around the table.
So we have 2 x 120 = 240 arrangements in which the Chief of Naval Operations and the Chief of the National Guard Bureau could sit together, if they were both willing to.
However, they are not both willing to sit next to each other. So we need to subtract those arrangements. 720 - 240 = 480.
So the correct answer is
B.
