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
Options: 56 , 64 , 65 , 316 , 560
Hmmm, this is an ambiguously-worded question.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
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
