the procedure will be in this way:
Number of non-negative integral solutions = 22C2
For finding X for divisible by 5:
X = 0 then Y + Z = 20 Number of non negative integral solutions = 21C1 = 21
X =5 then Y+ Z = 15 Number of non negative integral solutions = 16C1 = 16
X=10 then Y + Z = 10 Number of non negative integral solutions =11C1 = 11
X =15 then Y + Z = 5 Number of non negative integral solutions = 6C1 = 6
X =20 then Y + Z =0 Number of non negative integral solutions = 1C1 = 1
Sum of all these values = 21 + 16 + 11 + 6 + 1 = 55
Required probability = 55 / 22C2 = 5/21