Find the number of 4-digit numbers that can be formed using the digits 1,2,3,4,5 if no digit is repeated. How many of these will be even?

Explanation

Required number of 4-digit numbers
= number of arrangements of 5 digits taking 4 at a time
`= ""^(5)P_(4)=(5xx4xx3xx2)=120.`
Particular case To get an even number, the unit's digit is 2 or 4.
Thus, there are 2 ways of filling remaining 3 places with the remaining 4 digits `=""^(4)P_(3)=(4xx3xx2)=24.`
Hence, the required number of even numbers `=(2xx24)=48.`