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. 3/16
• B. 5/16
• C. 7/16
• D. 9/16

Answer 1

The correct option is C 7/16

Given,

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 $5$,

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

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 $5$,

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