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 1

Answer: (D)

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 $={}^n{C}_3+{}^n{C}_2$