the procedure will be in this way:
Number of non-negative integral solutions = ^{22}C_{2 }
For finding X for divisible by 5:
X = 0 then Y + Z = 20 Number of non negative integral solutions = ^{21}C_{1 }= 21
X =5 then Y+ Z = 15 Number of non negative integral solutions = ^{16}C_{1 } = 16
X=10 then Y + Z = 10 Number of non negative integral solutions =^{11}C_{1 } = 11
X =15 then Y + Z = 5 Number of non negative integral solutions = ^{6}C_{1 }= 6
X =20 then Y + Z =0 Number of non negative integral solutions = ^{1}C_{1} = 1
Sum of all these values = 21 + 16 + 11 + 6 + 1 = 55
Required probability = 55 / ^{22}C_{2} = 5/21