Question

How many four-digit numbers which are divisible by $4$ can be formed from the digits $1,2,3,4$ and $5$ considering each digit at most once?

Answer 1

A number is divisible by 4 if the last 2 numbers are divisible by 4 (divisible by 2 twice)
Ending can be
$12$
$24$
$32$
$42$
$52$
Case: Ending with $12,24,32,42,54$
First digit - $3$ choices
Second digit - $2$ choices
Third digit - $1$ choice
Fourth digit - $1$ choice
6 possible choices for each ending (e.g. $3412,3512,3212,4512,5312,5412$)
Total number of 4 digit numbers divisible by $4=6\times 5=30$