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# Doubt: How many ways can you arrange 10 non-identical balls in 4 ident

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Intern
Joined: 30 Aug 2017
Posts: 17
Concentration: Real Estate, Operations
Doubt: How many ways can you arrange 10 non-identical balls in 4 ident  [#permalink]

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21 Oct 2017, 13:27
1
How can I solve the below question without writing down the cases? If boxes were also non-identical, I know the answer will be 10^4. Is there any such formula for this case?

Q: How many ways can you arrange 10 non-identical balls in 4 identical boxes? (assuming 1 or more boxes can be empty)
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Joined: 02 Aug 2009
Posts: 6512
Re: Doubt: How many ways can you arrange 10 non-identical balls in 4 ident  [#permalink]

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21 Oct 2017, 22:07
Ace800 wrote:
How can I solve the below question without writing down the cases? If boxes were also non-identical, I know the answer will be 10^4. Is there any such formula for this case?

Q: How many ways can you arrange 10 non-identical balls in 4 identical boxes? (assuming 1 or more boxes can be empty)

hi..

this is going to be a lengthy calculation..

you have to look into different cases....
1) all 10 in one - 4 ways
2) 9 in one and 1 in second- so choose two out of 4.. 4C2

further carry on for different combinations .
https://gmatclub.com/forum/topic215915.html#p1667366
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2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

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Intern
Joined: 30 Aug 2017
Posts: 17
Concentration: Real Estate, Operations
Re: Doubt: How many ways can you arrange 10 non-identical balls in 4 ident  [#permalink]

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22 Oct 2017, 11:55
chetan2u wrote:
Ace800 wrote:
How can I solve the below question without writing down the cases? If boxes were also non-identical, I know the answer will be 10^4. Is there any such formula for this case?

Q: How many ways can you arrange 10 non-identical balls in 4 identical boxes? (assuming 1 or more boxes can be empty)

hi..

this is going to be a lengthy calculation..

you have to look into different cases....
1) all 10 in one - 4 ways
2) 9 in one and 1 in second- so choose two out of 4.. 4C2

further carry on for different combinations .
https://gmatclub.com/forum/topic215915.html#p1667366

Hi Chetan,

I was wondering if there was any formula that can be used instead of writing down each case. For instance:
if N Balls and P Baskets ( both identical )then ways=N
If N Balls and P Baskets (both non-identical) then ways= P^N
If Balls are identical but baskets are not, then ways= (N+P-1)!/N!(p-1)!

I am wondering if there is any such formula for this case as well which can be used readily instead of writing down each case?? I feel like there might be because the other cases all seem to have one..I just don't know what it is though...
Re: Doubt: How many ways can you arrange 10 non-identical balls in 4 ident &nbs [#permalink] 22 Oct 2017, 11:55
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