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

Question

Quantrex Academy · Accepted Answer

Correct answer: 45

If we take gap of 2 sides then from figure shown we have

{ }^4 \mathrm{C}_2

ways We can start with

1,2,3,4,5

so

5 \times{ }^4 \mathrm{C}_2=5 \times 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 \mathrm{C}_2

ways

In how many ways can a pair of parallel diagonals of a regular...