Question

The total number of $5$-digit numbers, formed by using the digits $1,2,3,5,6,7$ without repetition, which are multiple of $6$, is

• A. 36
• B. 48
• C. 60
• D. 72

Answer 1

Answer: (D)

To make a no. divisible by $3$ we can use the digits
$1,2,5,6,7$ or $1,2,3,5,7$
Using $1,2,5,6,7$, number of even numbers is
$=4\times 3\times 2\times 1\times 2=48$
Using $1,2,3,5,7$, number of even numbers is
$=4\times 3\times 2\times 1\times 1=24$
Required answer is $72$.