Question

The number of $4$ digit numbers that can be formed with $0,1,2,3,5$ which are divisible by $2$ or $5$ is

• A. $84$
• B. $60$
• C. $120$
• D. $53$

Answer 1

Answer: (B)

$60$

Considering $0,1,2,3,5$ and non repetitions of digits.
Number of four digit numbers divisible by $2$ or $5$ should contain $0,2$ or $5$ in the end of the number.
$\to$ _ _ _ 5
Implies $4(3!)$ numbers.
Now eliminating the numbers with $0$ at the starting, we get
$4(3!)-3!$
$=3(3!)$
$=18$. ...(i)

Implies $4(3!)$ numbers.
$=24$ ...(ii)

Implies $4(3!)$
Eliminating the numbers with $0$ at the starting, we get
$4(3!)-3!$
$=3(3!)$
$=18$ ...(ii)
Adding (i), (ii) and (iii), we get
$18+24+18$
$=36+24$
$=60$