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

Explanation

(i) Required number of 4 digit numbers by using digits `(1, 2, 3, 4, 5) = .^(5)P_(4)`
`=(5) (4) (3) (2) = 120`
(ii) For 4 digit even numbers, unit's place can be filled either with 2 or 4.
Let 2 be fixed at unit's place. Then the remaining three places are filled in `.^(4)P_(3)` ways
`= 4.3.2 = 24`
Similrly, there are 24 ways when unit's place is filled with 4.
`therefore` total number of 4 digited even numbers `= 24+24=48`