X|Y|Z
Number of ways to arrange 36 similar objects and 2 lines= 38!/36!2!
or you can remember the formula
\(x_1\)+\(x_2\).....+\(x_r\)= N
where \(x_1\), \(x_2\) ....... \(x_r\) are non-negative integers
Total integral solutions= (N+r-1) C (r-1)
In the above question N=36, and r=3
Anant2410 wrote:
Hovkial wrote:
We are given that:
X + Y + Z = 36.
The total number of solutions to this equation will be given by:
(36+3-1)C(3-1) = 38C2 = 703.
Note: "C" denotes combination.
The number of solutions where X will be equal to Y will be 19 [ from (X, Y) = (0, 0) to (18, 18)].
So, the number of solutions where X will not be equal to Y = 703 - 19 = 684.
Out of these 684 solutions, half of the solutions will have X > Y and the other half will have X < Y.
Hence, the total number of solutions where X will be greater than or equal to Y will be:
19 + (684/2) = 361.
Why are you doing 3-1 for combination?