Question

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

• A. 120
• B. 300
• C. 420
• D. 20

Answer 1

Answer: (C)

420

Answer 2

The units place can be filled in 4 ways as any one of 0, 2, 4 or 6 can be placed there. The remaining three places can be filled in with remaining 6 digits in $6P_{3}$ = 120 way. So, total number of ways = 4 × 120 = 480. But, this includes those numbers in which 0 is fixed in extreme left place. Numbers of such numbers

0	×	×	×
Fix	5P2 ways		3 ways (only 2, 4 or 6

∴ Required number of ways = 480 – 60 = 420.