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 $\left(\ge 3\right)$ distinct elements. The number of triplets (x, y, z) of the A elements in which at least two coordinates is equal to

1. A

2. B

${\mathrm{n}}^{3}{-}^{\mathrm{n}}{\mathrm{P}}_{3}$

3. C

$3{\mathrm{n}}^{2}-2\mathrm{n}$

4. D

$3{\mathrm{n}}^{2}\left(\mathrm{n}-1\right)$

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### Solution:

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

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