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

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

A
$^{n} P_{3}$
B
$n^{3} -^{n} P_{3}$
C
$3 n^{2} - 2 n$
D
$3 n^{2} (n - 1)$

Solution:

Total number of triplets without restriction is n x n x n. The number of triplets with all different coordinates is $^{n} P_{3}$ . Therefore, the required number of triplets is , $n^{3} - n_{P_{3}}$

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