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Study Stuff for MCA Examinations - NIMCET
Study Stuff for MCA Examinations - NIMCET
Previous Year Question (PYQs)
A person goes in for an examination in which there are four papers with a maximum of $m$ marks from each paper. The number of ways in which one can get $2m$ marks is
Solution
Let the marks in four papers be $x_1,x_2,x_3,x_4$ with
$0\le x_i\le m$ and
$x_1+x_2+x_3+x_4=2m$.
Number of non-negative solutions without restriction
$={}^{2m+3}C_3$.
Subtract cases where any $x_i>m$.
Using inclusion–exclusion, the required count simplifies to
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