Question

Number of numbers divisible by $25$ that can be formed without repetition using only the digits $1,2,3,4,5,0$ taken five at a time is

Answer 1

$1,2,3,4,5,0$
A number divisible by $25$ if the last two digits are $25$ or $50.$
Case $1:$ If the last two digits are $25$


So, number of possible numbers $=3\times 3\times 2=18$
(as first digit can not be zero)

Case $2:$ If the last two digits are $50$


So, number of possible numbers $=4\times 3\times 2=24$
Therefore, total possible numbers $=18+24=42$