Obviously with the given 5-digits, numbers greater than 5000 are either 4-digit numbers having 5 or 7 or 8 or 9 at the thousand’s place or 5-digit numbers.
Since the thousand’s place in the required 4-digit numbers cannot take 3 as a value, we have 4 options for thousand’s place, the remaining 4 out of 5 (1 earning the one used up at thousand’s place) for hundred’s place, 3 for tens’ place and 2 for one’s place.
(Note: Repetition of digits is not allowed)
Four-Digit Numbers
Thousands Place
5, 7, 8 or 9 |
Hundreds Place
Any of the 4 remaining digits |
Tens Place
Any of the remaining 3 digits |
Ones Place
Any of the remaining 2 digits |
| 4 ways |
4 ways |
3 ways |
2 ways |
∴ Number of 4-digit numbers greater than 5000
That can be formed with given digits = 4 × 4 × 3 × 2 = 96
For the 5-digit numbers, the various places can be filled up as shown:
∴ Number of 5-digit numbers = 5 × 4 × 3 × 2 × 1 = 120.
∴ Total required numbers = 96 + 120 = 216.
