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Question

In an examination,the maximum mark for each of the three papers is 50 and the maximum mark for the fourth paper is 100. The number of ways in which the candidate can score 60% marks in aggregate is :

A
125640
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B
110551
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C
97860
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D
None of these
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Solution

The correct option is B 110551
Let the marks scored by the candidate in four papers be x1,x2,x3,x4 then ,
x1+x2+x3+x4=150( i.e 60% of 250 is 150) where
0x1, x2, x350 and 0x4100;
The number of solution of equation is same as the
coeff. of x150 in (1+x+x2+x50)3(1+x+x2++x100)
=coeff. of x150 in (1x511x)3(1x1011x)
=coeff. of x150 in (1x51)3(1x101)(1x)4
=coeff. of x150 in (13x51+3x102x153)(1x101)×(1+ 4C3x+ 5C3x2+ 6C3x3)
= 153C33× 102C3+3× 51C3 52C3
=110551

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