How many one-one functions $f : \{1, 2, 3\} \to \{1, 2, 3, 4, 5, 6\}$ satisfy $f(1) < f(2) < f(3)$?

Explanation

1. 01

   A one-one $f$ takes 3 different values, and any 3 different values can be put in increasing order in exactly one way.

2. 02

   So each choice of 3 images out of 6 gives one such $f$: ${}^{6}C_{3} = 20$.