Question

Set A has 4 elements and set B has 3 elements. The elements of set A are mapped randomly with the elements of set B such that function $f:A\to B$ exists. The probability that the function is into, is

• A. $\frac{4}{9}$
• B. $\frac{5}{9}$
• C. $\frac{3}{4}$
• D. none of these

Answer 1

Answer: (B)

$\frac{5}{9}$

Total no. of functions = $3^4$
onto functions = $\frac{4.3}{2112}$
=$2^2{.3}^2$
Probability of into function =$1-\frac{2^2{.3}^2}{3^4}=\frac{5}{9}$