Question: Committee of 4 people

Comment on Committee of 4 people

why cant we calculate it like: 8*7*6*5?
gmat-admin's picture

You are breaking the task into 4 stages (select 1st student, select 2nd student, select 3rd student and select 4th student).

HOWEVER, when you do this, you should ask "Does the outcome of each stage differ from the outcomes of the other stages?" (for more on this, watch:

In this case the answer is no; each selected person gets to be on the committee. That is, selecting A then D then E then B, is the SAME as selecting E then B then A then D

As such, we cannot use the stages approach. Instead, we must use combinations.

Hi Brent!!
can you help me please on this one ?
in how many ways can 12 different books be distributed equally among 4 different boxes?
i will really appreciate it!!
gmat-admin's picture

Here's my full solution:

For some reason, the 5 posts above mine all have the same wrong solution. As you can see from my solution, we can distinguish the 4 boxes by naming them box #1, box #2, box #3, and box #4. So, there's no need to multiply our answer by 4! at the end (as all of the 5 other posts have done)


The question says that - 2 notepads and 4 colors

1st set - 1 notepad and 3 different colors
2nd set - 1 notepad and 3 same colors

Here we have to understand that - he can reselect the same pad.

what if he is not allowed to reselect, and the second pad has to be the next one.

Then in that case - 2 * 4 + 1 * 4 = 12

Is this correct?
gmat-admin's picture

Question link:

If the notepads must be DIFFERENT sizes, then the question is impossible to solve.
There are only TWO sizes (say large and small)

In the original question, we're selecting groups of THREE notepads. Since there are only TWO different sizes (large and small), there's no way for all three notepads to be different sizes.

Does that help?

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