Permutations and Combinations

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LetS={1,2,3,4,5,6}andXbe the set of all relationsRfromSto S that satisfy both the following properties:
i.‌‌Rhas exactly 6 elements.
ii. For each(a,b)∈R, we have|a−b|≥2.
LetY={R∈X: The range of R has exactly one element}and
Z={R∈X:Ris a function from S toS}.
Letn(A)denote the number of elements in a SetA.