Ok, so this isn't a GMAT question per se, but I don't see how it couldn't theoretically appear on a test in the future.
How many ways can we place 7 identical balls into 8 separate (but
distinguishable) boxes?
Now to be fair, multiple choice answers would help us to the solution but there could also be trick answers so I am trying to solve this problem without "assistance" from answer choices (plus there are no multiple choice questions lol).
[spoiler]The solution, as given from an outside source, says it boils down to a simple combination with repetition allowed problem. So C(n+k-1, k)
If n = 8 and k = 7
(8+7-1)!/7!(8+7-1-7)!= 14!/7!7! = total number of ways of placing 7 identical balls into 8 distinct boxes[/spoiler]
Solution is above but I have some questions.
For starters, is this even fair game for the GMAT?
Secondly, how do we determine n and k in this situation? I can't wrap my head around it....
I tried to suppose that instead of boxes and balls, it was, say, the set of ABCDEFGHIIIIIII (8 distinct letters and 7 identical)
which at least made it easier to conceptualize, it's a combination of 15 elements with 7 repeating items and then I realized, I have NO clue of what is being selected and what it is being selected from...
If this is useless then sorry for wasting your time and I will ignore combinations with repetition for GMAT purposes at least =).
How many ways can we place 7 identical balls into 8 separate (but
distinguishable) boxes?
Now to be fair, multiple choice answers would help us to the solution but there could also be trick answers so I am trying to solve this problem without "assistance" from answer choices (plus there are no multiple choice questions lol).
[spoiler]The solution, as given from an outside source, says it boils down to a simple combination with repetition allowed problem. So C(n+k-1, k)
If n = 8 and k = 7
(8+7-1)!/7!(8+7-1-7)!= 14!/7!7! = total number of ways of placing 7 identical balls into 8 distinct boxes[/spoiler]
Solution is above but I have some questions.
For starters, is this even fair game for the GMAT?
Secondly, how do we determine n and k in this situation? I can't wrap my head around it....
I tried to suppose that instead of boxes and balls, it was, say, the set of ABCDEFGHIIIIIII (8 distinct letters and 7 identical)
which at least made it easier to conceptualize, it's a combination of 15 elements with 7 repeating items and then I realized, I have NO clue of what is being selected and what it is being selected from...
If this is useless then sorry for wasting your time and I will ignore combinations with repetition for GMAT purposes at least =).
