A probability problem by Mayank Gupta
Probability
Level
2
Three variables x,y,z have a sum of 30. All three of them are non-negative integers.If any two variables don't have the same value and exactly one variable has a value less than or equal to three , then find the number of possible solutions for the variables.
294
285
98
68
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1 solution
As we know that x+y+z=30 and x,y,z>0 and x,y,z is not equal to 0. now ... make 3 cases:- case 1.) if x=1,,, then y+z=29 1.) then y=1 and z=28, 2,) then y=2 and z=27, ... ...... .... .....
.... 28.) then y=28 and z=1. total no of cases adds upto 28 here..
similarly .. make cases if x=2.. and x=3.. then assuming that x can be any of the x,y,z.. we easily get the answer by just suming up the cases .. which we get 294.. :)