Parenthesization/Examples/2

Example of Parenthesization
A word of $2$ elements can be parenthesized in only $1$ distinct way:
 * $\quad \paren {a_1 a_2}$

Proof
From Number of Distinct Parenthesizations on Word, the number of distinct parenthesizations of a word $w$ of $n$ elements is the Catalan number $C_{n - 1}$:
 * $C_{n - 1} = \dfrac 1 n \dbinom {2 \paren {n - 1} } {n - 1}$

For $n = 2$ we have: