Three numbers are chosen at random from 1 to 20 , then the probability that the sum of three numbers is divisible by 3 is

Step-by-step solution

Total number ways we can choose three integers from 20 integers = ²⁰ C₃ (I) We will get all three integers are multiple of three (3,6,9,12,15,18)= ^6 C₃ (II) We will get sum divisible by 3, if all three numbers when divided by 3 givens remainder of 1(1,4,7,10 , 13,16,19)= ^7 C₃ (III) We will get sum divisible by , if all three numbers are when divided by 3, gives a remainder of 2(2,5 , 8,11,14,17,20)= ^7 C₃ (IV) We will get sum divisible by 3, if one of themis divisible by 3, one of them when divided by 3 gives a r