Q) A = number of ways 25 marbles can be placed in 6 bowls, such that at least one bowl has 5 or more

marbles.

B = number of ways 25 marbles can be placed in 6 bowls

Answer is C

I find B using 25c6 = 177100

For A, the bowl with min 5 can have max 20 marbles (since having more would lead to at least 1 bowl not being used) which is 16 possible choices and multiply that with 20c5. This is obviously incorrect.

Princeton Review-Supplemental questions to their GRE guide

So what’s the question? Not clear from what you’re said.

Hint: show that the two quantities are the same.

The question asks us to compare quantities A and B. Th answer choice (C) indicates that they are equal.

i am unable to show that the 2 quantities are the same and hence am seeking the help of this forum .

My workings are shown above, following which i am UNABLE to show that they are equal. Could you perhaps point out where i am going wrong ?

Here’s the hint: you don’t need any maths for this one, and I wouldn’t recommend it even if you could for the below reason.

Show that “number of ways 25 marbles can be placed in 6 bowls, such that at least one bowl has 5 or more marbles” *literally* means “number of ways 25 marbles can be placed in 6 bowls”. In other words, show that “at least one bowl has 5 or more marbles” is useless.

Thank you!

I get it now, any arrangement with 6 bowls with each bowl being utilized will require 1 bowl w 5 or more marbles.