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shefali sharma Grade: 12
        

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

Answers : (1)

Badiuddin askIITians.ismu Expert
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


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Badiuddin


 

7 years ago
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