IIT JEE , AIEEE Forum - Mathematics , Algebra

raja987654321

In an examination , the maximum marks for each of the three papers is 50 each. The maximum marks for the fourth paper is 100 . Find the number of ways a student can score 60% in aggregate .

rajatsen91

60% = 90
so a+b+c+d = 90
a<50
b<50
c<50
d<100
let l = 50-a
m = 50-b
n= 50-c
o = 100-d
so, putting these values
l+m+n+o=160
now all we have to do is to find the number of non negative integral solutions of these
= (160+4-1)C160
=163C160 = 163C3 = 708561
RATE ME

raja987654321

the correct answer is given as 1,10,551 Although whenever i m solving its coming out as 176851

rajatsen91

this can be solved using generating.
(x^0++x^1+x+2.................+x^50)^3+(x^0+x^1..........+x^100)
= (1(x^51-1)/(x-1))^3 +(x^101-1)/x-1
now expand both sides binomially and check for the coeff of x^90
that will be the answer

raja987654321

soln is perfect !

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