Problem Solving

RBBmba@2014 wrote:In how many ways can a person post 5 letters in 4 letter boxes ?

(A) 120
(B) 600
(C) 2400
(D) 4^5
(E) 5^5

OA: D

Take the task of distributing the 5 letters and break it into stages.

Stage 1: Select a box for the 1st letter to go into.
There are 4 available boxes, so we can complete stage 1 in 4 ways

Stage 2: Select a box for the 2nd letter to go into.
There are 4 available boxes, so we can complete stage 2 in 4 ways

Stage 3: Select a box for the 3rd letter to go into.
There are 4 available boxes, so we can complete stage 3 in 4 ways

Stage 4: Select a box for the 4th letter to go into.
There are 4 available boxes, so we can complete stage 4 in 4 ways

Stage 5: Select a box for the 5th letter to go into.
There are 4 available boxes, so we can complete stage 5 in 4 ways

By the Fundamental Counting Principle (FCP), we can complete all 5 stages (and thus distribute all 5 letters) in (4)(4)(4)(4)(4) ways ([spoiler]= 4� ways[/spoiler])

Answer: D
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Note: the FCP can be used to solve the MAJORITY of counting questions on the GMAT. For more information about the FCP, watch our free video: https://www.gmatprepnow.com/module/gmat-counting?id=775

Then you can try solving the following questions:

EASY
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MEDIUM
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DIFFICULT
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Cheers,
Brent

madhusudhan237 wrote:HI Brent

In your post, you have considered like: for each letter to get posted, there are 4 letter boxes available.

But, why not in such a way that - I have 4 letter boxes available & 5 letters to post?

In that case,

---------- ---------- ----------- -----------
Letter box-1 Letter box-2 Letter box-3 Letter box-4

So, to post 5 letters

Case1: Letter box-1 has 5 ways (all 5 letters available)
Case2: Letter box-2 has 4 ways (since, only 4 letters are available, one already posted in letter box-1)

Similarly,
Case3, Case4 will have 3, 2 ways

Total (by FCP rule) = 5 x 4 x 3 x 2 = 120 ways

I know, I am wrong! But, I am trying to get into the grove of right thinking

Thanks for your clarification!

Madhu

[/list]

Your solution assumes that each letter box must one letter.
To avoid this problem, try to be very clear what is happening with each stage.
In your solution, you write: Case1: Letter box-1 has 5 ways
What does this mean?

If you had written, "stage 1: select a letter to go into mailbox 1," you might have seen the problem with this approach, because there's nothing that says mailbox 1 must contain a letter.

Cheers,
Brent