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```        a man goes for an examination in which there are 4 papers with maximum marks'm' for each paper then no of ways of getting 2m marks:
ans. (m+1)(2m^2+4m+3)/3```
7 years ago

147 Points
```										Dear shefali
let the markd in the 4 papers are x,y,z,w
where 0≤x,y,z,w≤m
x+y+z+w=2m
now our task is to find out the intiger solution of this equation in given condition.
number of solution is   = 2m+4-1C4-1=2m+3C3
but this solution also include those solution in which any variable is greater than m
so we have to subtact those solution
for  x ≥ m+1 .
let  t=x-(m+1)     t≥o
x+y+z+w=2m
t+y+z+w=m -1
solution of this equation = m-1+4-1C4-1=m+2C3
similerly for y ≥ m+1,z ≥ m+1,w ≥ m+1
so final solution =2m+3C3 -4*m+2C3
=(m+1)(2m^2+4m+3)/3
Please feel free to post as many doubts on our discussion forum as you can.If you find any question Difficult to understand - post it here and we will get you the answer and detailed  solution very  quickly. We are all IITians and here to help you in your IIT JEE preparation.All the best. Regards,Askiitians ExpertsBadiuddin

```
7 years ago
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