eski wrote:Q. How many ways 7 sweets can be given to A , B and C . If A receieves 2 sweets and B &C receive one each.

Options: 56 , 64 , 65 , 316 , 560

Hmmm, this is an ambiguously-worded question.
I'm assuming that the 7 treats are unique (different from each other) and that person A gets exactly 2 treats, person B gets exactly 1 treat, and person C gets exactly 1 treat. If this assumption is correct, then here's one approach:

Take the task of distributing 4 treats and break it into stages.

Stage 1: Give person A two treats.
Since the order in which we give person A the 2 treats does not matter, this stage can be appoached using combinations.
There are 7 treats and we must select (choose) two for person A to receive.
This can be accomplished in 7C2 ways (21 ways)

Aside: If anyone is interested, we have a free video on calculating combinations in your head: https://www.gmatprepnow.com/module/gmat-counting?id=789

Stage 2: Give person B one treats.
After giving person A two treats, there are now 5 treats remaining.
So, we can accomplish this stage in 5 ways

Stage 3: Give person C one treats.
There are now 4 treats remaining.
So, we can accomplish this stage in 4 ways

By the Fundamental Counting Principle (FCP) we can complete all 3 stages (and thus distribute 4 treats to the 3 people) in (21)(5)(4) ways (= 420 ways)

Hmmm, this doesn't match any of the answer choices. Perhaps my assumptions were wrong.

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

My answer was the same as Brent's, but the question is so badly worded, it's hard to tell what it means.

Incidentally, this isn't the 'style' of counting question the GMAT asks. I'd suggest you work with material that more closely resembles what you'll see on the real test.