Question

How many three digit can be formed using the digits $1,2,3,4,5,$ without repetition of digits$?$ How many of these are even$?$

Answer 1

Three places are to be filled with $5$ different objects.
$\therefore$ Number of ways${=}^5{\text{P}}_3=5\times 4\times 3=60$

For the 2nd part, unit digit can be filled in two ways & the remaining two digits can be filled in ${}^4{\text{P}}_2$ ways.
$\therefore$ Number of even numbers$=2{\times }^4{\text{P}}_2=24.$