Question

A ten digit number is formed using the digits from zero to nine, every digit being used exactly once.The probability that the number is divisible by $5$ is

• A. $\frac{14}{81}$
• B. $\frac{15}{81}$
• C. $\frac{16}{81}$
• D. $\frac{17}{81}$

Answer 1

The correct option is D $\frac{17}{81}$

Conditions of forming such a number-
1) All the digits have to be used at once
2) 0 should not come at first place
3) last digit should be either $0$ or $5$
case 1) numbers ending with $0=$ $9!$
case 2) numbers ending with $5=$$(9!-8!)$ {numbers starting with 0 are subtracted}
total $10$ digit numbers that can be formed = $10!-9!$
$P=17/81$