The numbers 1,2,…,17 are divided into 5 disjoint sets. One set has 5 elements, one set has 4 elements, two sets have 3 elements and the last set contains the 2 remaining elements. Two players each choose a number from 1 to 17 at random. The probability they choose numbers from the same set can be expressed as a/b, where a and b are coprime positive integers. What is the value of a+b?

Answer 1

Hmmm. For each set of size n, there's a n/17 chance that each person picked a number from that set.

(5/17)^2 + (4/17)^2 + 2(3/17)^2 + (2/17)^2 = 63/289

Answer 2

352

Answer 3

Which set or sets 1/9 belongs to