Permutations and Combinations

Let A={a,b,c,d,e,f}
R⊂A×A,R is reflexive, ⇒(x,x)∈R‌∀x∈R
⇒(‌6C1)⇒6 elements
We need 4 elements but since R is symmetric, we want to pairs (α,β) and (γ,δ) such that (α,β)∈R and (γ,δ)⇒(β,α)∈R and (δ,γ)∈R
⇒ We need to choose the pairs
(α,β) and (γ,δ)
⇒ Total unordered pairs
⇒‌6C2=15 pairs
Out of these we need two pairs
⇒‌‌‌15C2=‌

15×14

2

=105