In how many ways can a pair of parallel diagonals of a regular polygon of 10 sides be selected

Step-by-step solution

If we take gap of 2 sides then from figure shown we have ^4 C ₂ ways We can start with 1,2,3,4,5 so 5 ^4 C ₂=5 6=30 ways Now take 1 with 4 (gap of 3 sides) then we have 3 diagonals which are 14,510,69 so we have ^3 C ₂ ways