Question

If F is the set of all onto functions from a set of vowels to set having 3 elements and $f\in F$ is chosen randomly ,then the probability that $f^{-1}\left(x\right)$ is a singleton is

• A. $\frac{7}{15}$
• B. $\frac{8}{15}$
• C. $\frac{9}{15}$
• D. $\frac{10}{15}$

Answer 1

The correct option is A $\frac{7}{15}$

No.of onto functions from A having 5 elements to set B having 3 elements is 150 we shall now count onto function which satisfy $f^{-1}\left(x\right)$ is singleton. We can choose a singleton in $5_{C_1}$ ways . The remain 4 elements can be mapped to remaining 2 elements in $2^4-2=14$ ways
$\therefore$ desired prob= $\frac{5\left(14\right)}{150}=\frac{7}{15}$