Question

Let $X$ and $Y$ denote the sets containing 2 and 20 distinct objects respectively and $F$ denote the set of all possible functions defined from $X$ and $Y$. Let $f$ be randomly chosen from $F$. The probability of $f$ being one-to-one is

• A. 0.95

Answer 1

The correct option is A 0.95

Total possible funcitons $={20}^2=400$
Number of one-to-one functions
$=20P_2=20\times 19$
$\therefore$ Required probability $=\frac{20\times 19}{20\times 20}=0.95$