Wrong answer and reasoning..

3 votes

The number of ways can 10 balls be selected from urn contain 10 identical red balls 5 identical green balls and 3 identical blue balls ?

2 votes

Best answer

24 is correct

how to solve pls refer this one detail explaination https://gateoverflow.in/65803/find-number-integral-solutions-using-generating-function?show=65803#q65803

1 vote

x+y+z =10

Number of way will be 10+3-1 C 3-1 = 66

Of all these 66 cases some are not valid

The conditions are x>=11, y>=6 , z>=4

Now x >=11 will be for 0 cases

Now y>=6 will be for x+y'+z = 10-6=4 so 4+3-1C 3-1= 15

Now z>=4 will be for x+y+z'= 10-4=6 so 6+3-1C3-1 = 28

But the conditions of y and z can be not valid when y=6 and z=4 is 1 way , this should be added as it will be subtracted for both y and z twice so the answer is 66-15-28+1= 24

Number of way will be 10+3-1 C 3-1 = 66

Of all these 66 cases some are not valid

The conditions are x>=11, y>=6 , z>=4

Now x >=11 will be for 0 cases

Now y>=6 will be for x+y'+z = 10-6=4 so 4+3-1C 3-1= 15

Now z>=4 will be for x+y+z'= 10-4=6 so 6+3-1C3-1 = 28

But the conditions of y and z can be not valid when y=6 and z=4 is 1 way , this should be added as it will be subtracted for both y and z twice so the answer is 66-15-28+1= 24

0

as i know whenever more than 1 upper constraints given then we use generating function .. complement method is not correct for more than 1 upper constraints

1

@vyas why complement will not be true,..can u say by giving example..I think this is correct

@jain that is for number of non negative integer solutions for the equation

@jain that is for number of non negative integer solutions for the equation