The number of 4 digit even numbers that can be formed using 0, 1, 2, 3, 4, 5, 6 without repitition is

Let AB C Drepresent the 4digit number.
The placeD can be filled with any of the 0, 2, 4, 6 in 4 different ways.
The other 3 places can be filled in 6 × 5 × 4 ways.
Hence, total number of ways = 4 × 6 × 5 × 4 = 480
But, this inclides numbers such that position A is filled with 0
No. of such numbers = 1 × 3 × 5 × 4 = 60
Hence, required no. of ways = 480 - 60 = 420
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