apoorva.srivastva wrote:Six students are equally divided into 3 groups, then, the three groups were assigned to three different
topics. How many different arrangements are possible?
(A) 30
(B) 60
(C) 90
(D) 180
(E) 540
Here's my edited response.
Let's say we have 3 topics: Topic A, Topic B and Topic C.
Our goal is to assign 2 people to each topic.
Let's take this task and break it into stages.
Stage 1: Select 2 people for Topic A.
Since the order in which we select these people does not matter (e.g., selecting Joe then Al is the same as selecting Al then Joe), we can use combinations.
There are 6 people, and we must select 2. This can be accomplished in 6C2 ways (
15 ways).
Stage 2: Select 2 people for Topic B.
Once again, order does not matter.
There are 4 people remaining, and we must select 2. This can be accomplished in 4C2 ways (
6 ways).
Stage 3: Select 2 people for Topic C.
There are only 2 people remaining, so this can be accomplished in
1 way
By the Fundamental Counting Principle (FCP) we can complete all 3 stages (and thus assign 2 people to each topic) in
(6)(5)(1) ways ([spoiler]= 90 ways[/spoiler])
Cheers,
Brent
Aside: For more information about the FCP, we have a free video on the subject:
https://www.gmatprepnow.com/module/gmat-counting?id=775
If anyone is interested, we have a free video on calculating combinations (like 6C2) in your head:
https://www.gmatprepnow.com/module/gmat-counting?id=789
