Question

$5$ digit numbers are formed by using $0,1,2,3,4,5$. The probability that the selected number is divisible by $6$ is

• A. $\frac{9}{100}$
• B. $\frac{9}{25}$
• C. $\frac{9}{50}$
• D. $\frac{3}{50}$

Answer 1

The correct option is C $\frac{9}{50}$

If a number is divisible by $6$, number should end with even number and sum of digits should be divisible by $3$. Therefore either $3$ or $0$ can be excluded
Total number of cases$=5\ast 5!$
Favorable Cases excluding $0=2\ast 4!$ (ending with $2$ or $4$)
Favorable Cases excluding $3=2\ast 3\ast 3!$ (ending with $2$ or $4$ )
Favorable Cases excluding $3=4!$ (ending with $0$ )
Probability that the selected number is divisible by $6=(2\ast 4!+6\ast 3!+4!)/(5\ast 5!)$
$=9/50$