Question

How many numbers of three digits can be formed using the digits 1, 2, 3, 4, 5, without repetition of digits is x. How many of these are even is y.Find x + y.

Answer 1

Three places are to be filled with 5 different objects.
$\therefore$ Number of ways ${=}^5{P}_3=5\times 4\times 3=60$
For even numbers unit digit can be filled in two ways & the remaining two digits can be filled in ${}^4{P}_2$ ways.
$\therefore$ Number of even numbers $=2{\times }^4{P}_2=24$