Question

A function is selected randomly from the set of functions defined from set $A$ to set $B$, where $n\left(A\right)=4$ and $n\left(B\right)=7$. Then the probability that the selected function is not injection, is

• A. $\frac{223}{343}$
• B. $\frac{120}{343}$
• C. $\frac{210}{343}$
• D. $\frac{123}{343}$

Answer 1

The correct option is A $\frac{223}{343}$

$n\left(A\right)=4$ and $n\left(B\right)=7$ and $f:A\to B$
$P(f\text{is not one-one)}=1-P(f\text{is one-one)}$
$=[1-\frac{{(}^7{\text{p}}_4)}{\left(7^4\right)}]=[1-\frac{7\cdot 6\cdot 5\cdot 4}{7^4}]=\left(\frac{343-120}{343}\right)=\frac{223}{343}$