Question

Let $A\equiv \{1,2,3,4\},B\equiv \{a,b,c\}$, then number of function from $A\to B$, which are not onto is

• A. $9$
• B. $24$
• C. $45$
• D. $6$

Answer 1

Answer: (A)

$9$

$A\equiv \{1,2,3,4\}$

$B\equiv \{a,b,c\}$

Total function $(A\to B)$

$\text{Total onto function}(A\to B)$

$=4c_3\times 3!\times 3$

$=\frac{4!}{3!1!}\times 3!\times 3$

$=41\times 3=72$

Hence, no. of $f^n$ which are not onto

$=81-72$

$=9$