First slide

Permutations

Question

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

Moderate

A

$^{n} P_{3}$
B

$n^{3} -^{n} P_{3}$
C

${3n}^{2} - 2 n$
D

$3 n^{2} (n - 1)$

Solution

Total number of triplets without restriction is $n \times n \times n$ .
The number of triplets with all different coordinates is ⁿP₃.
Therefore, the required number of triplets is $n^{3} - n (n - 1) (n - 2)$ .

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