Question

The number of ways of choosing triplets (x, y , z) such that $z\ge max$ {x, y} and $x,y,z\in \{1,2,...,n\}$ is

• A. ${}^{n+1}{C}_3{+}^{n+2}{C}_3$
• B. $n(n+1)(2n+1)$
• C. $1^1+2^2+...+(n-1{)}^2$
• D. $2{\cdot }^n{C}_3$

Answer 1

The correct option is D $2{\cdot }^n{C}_3$

ways of choosing triplets (x, y , z)

$z\ge max$ {x, y} and $x,y,z\in \{1,2,...,n\}$

No. of ways of choosing this is $2{\times }^n{\text{C}}_3$

as value of x and y can be interchanged