The triplet ((x, y, z)) is chosen from the set (\\{1,2,3,...... | Mathematics | SolveeIt | Solveeit

Today, August 18

Question

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

A

$n^{3}$

B

$^{n}C_{3}$

C

$^{n}C_{2}$

D

$^{n}C_{2} + \,^{n}C_{3}$

Answer

$^{n}C_{2} + \,^{n}C_{3}$

Explanation

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 $= \,^{n}C_{3} + \,^{n}C_{2}$