1. Tardigrade
  2. Question
  3. Mathematics
  4. Let A be a set of n(≥ 3) distinct elements. The number of triplets (x, y, z) of the elements of A in which at least two coordinates are equal to

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Q. Let $A$ be a set of $n(\geq 3)$ distinct elements. The number of triplets $(x, y, z)$ of the elements of $A$ in which at least two coordinates are equal to

Permutations and Combinations

Solution:

Total number of triplets without restriction $=n \times n \times n .$
The number of triplets with all different coordinates $={ }^{n} P_{3}$
$\therefore $ The required number of triplets $=n^{3}-n(n-1)(n-2)$