How many ways are there to select (combinations) $n$ objects from $a$ identical objects of first kind, $b$ identical objects of second kind, $c$ identical objects of third kind and $d$ identical objects of fourth kind? P.S. : Since the maximum number of any kind is restricted it is different from the original stars and bars problem where there is no restriction.
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1Don't you mean "d identical objects of fourth kind"? – Ove Ahlman Jun 15 '15 at 06:42
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yes,thank you.I have corrected it. – ashiwn Jun 15 '15 at 06:45
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Related to http://math.stackexchange.com/questions/686/combinations-of-selecting-n-objects-with-k-different-types – OnceUponACrinoid Jun 15 '15 at 07:06
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@OnceUponACrinoid thankyou,the answers almost the same concept – ashiwn Jun 15 '15 at 10:52
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I figured out the answer. The question same as,
The total no of non negative integral solutions of x+y+z+w=n , where,
$0\le x\le a,0\le y\le b\ ,\ 0 \le z\le c\ $ and $\ 0\le w\le d$
changing variables as, x1=a-x,y1=a-y,z1=a-z and w1=a-w,
we get the answer to be, number of solutions of the equation x1+y1+z1+w1=a+b+c+d-n
answer= $$\binom{a+b+c+d-n+4-1}{4-1}$$
