Question: In how many ways can 7 identical erasers be distributed among 4 kids in such a way that each kid gets atleast one eraser but nobody gets more than 3 erasers?

1. 13
2. 14
3. 15
4. 16
5. 20

Answer:

Approach Solution (1):

Each kid has to get atleast one eraser so we give away 4 erasers to 4 kids. Now we are left with 3 erasers for 4 kids.

They can be given away in 2 ways:

Case 1: 1 – 1 – 1

3 kids get one eraser each in 4C3 ways= 4 ways (select 3 kids of the 4 who will get erasers)

Case 2: 2 – 1

One kid gets 2 erasers and another gets 1 in 4C1 * 3C1 = 12 ways
In all we have 4 + 12 = 16 ways to distribute erasers.

Correct Option: D

Approach Solution (2):

Each kid must get atleast 1 eraser and all erasers are identical. So there is only one way on which we can distribute 4 erasers to 4 kids.
Now, we are left with 3 erasers that need to be distributed among 4 kids
Since no student can get more than 3 erasers, we can’t give the remaining 3 erasers to noe student only.

Therefore, 2 cases are possible:

Case 1:

1 eraser each is given to 3 students:
Number of possible ways = 4C3 = 4

Case 2:

1 eraser is given to 1 student and 2 erasers are given to another student:
Number of possible ways = 4C1 * 3C1 = 4 * 3 = 12
Total number of ways = 12 + 4 = 16

Correct Option: D

“In how many ways can 7 identical erasers be distributed among 4 kids in such a way that each kid gets atleast one eraser but nobody gets more than 3 erasers?”- is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book “GMAT Official Guide Quantitative Review”. To solve GMAT Problem Solving questions a student must have knowledge about a good amount of qualitative skills. The GMAT Quant topic in the problem-solving part requires calculative mathematical problems that should be solved with proper mathematical knowledge.

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