Question

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

• A. $\frac{3}{16}$
• B. $\frac{5}{16}$
• C. $\frac{7}{16}$
• D. $\frac{9}{16}$

Answer 1

Answer: (C)

$\frac{7}{16}$

No. of five digit numbers $=(0,2,4,5,7)$

$4\times 4!$ numbers,

$4\times 4\times 3\times 2\times 1=4\times 24=96$

No. of numbers divisible by $5$,

$\bullet$ Ending with $0$ are, $4!=24$

$\bullet$ Ending with $5$ are, $3\times 3!=18$

No. of numbers divisible by $5$ are $18+24=42$

Probability that the number is divisible by $5$,

$=\frac{42}{96}=\frac{14}{32}=\frac{7}{16}$