In how many ways can two distinct subsets of the set A of k…

Maths Permutations & Combination JEE (Main) / AIEEE Problems (Previous Years) Subjective Type

Published on: August 13, 2026

In how many ways can two distinct subsets of the set A of k(k ≥ 2) elements be selected so that they have exactly two common elements.

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( k–2 –1)

Sol. Let the two subset be A & B

First select two element in k C 2 ways

Now remaining 'r' element for subset A are selected from (k – 2) elements and number of element for B from k – 2 – r elements

0 ≤ r ≤ k – 2

number of selection = k–2 C r .2 k–2–r

total number of selection

– 1,

Now every pair A, B is appearing twice

k C 2

((2 + 1) k–2 –1)

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