Five digited numbers are formed using $\{0,2,4,5,7\}$ without repetetion. One number is selected at random. The probability that it is divisible by 5 is

Five digited numbers are formed using $\{0,2,4,5,7\}$ without repetetion

$n\left(S\right)=4\left(4!\right)=4\times 24=96$

$E= selected number is divisible by 5$

$n\left(E\right)=numbers ending with 0+ numbers ending with 5$

$n\left(E\right)=4!+3\left(3!\right)=24+18=42$

$P\left(E\right)=\frac{42}{96}=\frac{7}{16}$