Three numbers are chosen at random from the set {0,1,2,....,29} without replacement. The probability that the sum of these numbers is 30 is:

(a)5/812

(b)15/812

(c)5/406

(d)3/406

Toatl possiblities ³⁰C₃
For sum 30
Start from first triad 0 1 29
Fix 0 and increase second number by 1 and decrease other by 1 till first number becomes 14 as after that repetion will start occuring
Total of 14 cases

Now increase 0 to 1 and fix it take second number 2 third 27
Again increase 2^nd number by 1 and second number decrease by 1 till 2^nd number become 14 and third becomes 15 after this repetition will occur
Total casses 13

Now start with triad 2 3 25
Make ensure you are taking second and third numbers greater then or equal to first to avoid repetition
In this total cases will be 11

You can proceed like this till first number number become 9 for that only case will be ther i.e. 9 10 11

You will get a total of 75 cases and you can find tthe required probability
Just follow this if you are unable to understand please repost.