1. Tardigrade
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  4. The triplet (x, y, z) is chosen from the set 1,2,3,... n such that x le y < z. The number of such triplets is

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Q. The triplet $(x, y, z)$ is chosen from the set $\{1,2,3,... n\}$, such that $x \le y < z$. The number of such triplets is

Permutations and Combinations

Solution:

Number of selections when $x < y < z$ is $^{n}C_{3}$.
Number of selections when $x = y < z$ is $^{n}C_{2}$.
$\therefore $ Required number $ = \,{}^{n}C_{3} + \,{}^{n}C_{2}$