Three variables x,y,z have sum of 30.All three of them are non-negetive integers.If any two variables don't have same value and extacly one variable has a value less han or equal to three,then find the number of possible solution for variables.; Three variables x,y,z have sum of 30.All three of them are non-negetive integers.If any two variables don't have same value and extacly one variable has a value less han or equal to three,then find the number of possible solution for variables.
Answers
Answer:
X+Y+Z=30 ; given any one of the number ranges from 0-3 and all other numbers start from 4. Hence consider the following equations:
X=0 ; Y+Z=30 The solution of the above equation is obtained from (n-1)C(r-1) formula. Total solutions obtained = 29 of which (y,z): (2,27)(27,2)(2,28)(28,2)(1,29)(29,1) must not be counted since they contain 1,2,3 as a part of solution. So, total number of ways= 29-6= 23 ways.
X=1; Y+Z=29 Total solutions obtained = 28 of which (y,z): (2,27)(27,2)(1,28)(28,1)(3,26)(26,3) must not be counted since they contain 1,2,3 as a part of solution. So, total number of ways= 28-6= 22ways.
X=2 ; Y+Z=28 Total solutions obtained = 27 of which (y,z): (1,27)(27,1)(2,26)(26,2)(3,25)(25,3) must not be counted since they contain 1,2,3 as a part of solution. So, total number of ways= 27-6= 21ways.
X=3 ; Y+Z= 27 Total solutions obtained = 26 of which (y,z): (1,26)(26,1)(2,25)(25,2)(3,24)(24,3) must not be counted since they contain 1,2,3 as a part of solution. So, total number of ways= 26-6= 20 ways.
Total number of ways = 23+22+21+20 = 84 ways
Total number of ways considering X,Y and Z = 84*3 = 252.