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Stars and Bars with Restriction

I just encountered the stars and bars technique page on Brilliant. https://brilliant.org/assessment/techniques-trainer/stars-and-bars/

The example problem asks How many ordered sets of non-negative integers are there such that \(a + b + c + d = 10\)

I was wondering, If an upper limit is placed on one or two of the variables, for example if \(a<5\) and \(b<4\), then how will the solution change?

Note by Sameer Jain
4 years, 2 months ago

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4 votes

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Okay brother the solution is simple First find the no of solutions without any restriction Now you have to subtract 3 cases, Case 1 When a =5 then the solve b+c+d=5; Case 2 When b=4; Case 3 When both a and b are at their maximas.; Subtract these cases from your solution. PS- case 3 is not valid in this case.

Raghav Bakshi - 3 years, 11 months ago

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