The number of integers, greater than 7000 that can be formed, using the digits 3,5,6,7,8 without repetition, is
- A.48
- B.168
- C.220
- D.120
Show answer and solution
Correct option: B
Solution
For a number greater than 7000, consider two cases:
4-digit numbers > 7000: The thousands digit must be 7, 8 (digits ≥ 7 from the set). That gives 2 choices for the first digit, then 4×3×2 = 24 arrangements for the remaining 3 digits. Total: 2 × 24 = 48.
5-digit numbers: All 5-digit numbers using 3,5,6,7,8 without repetition are automatically > 7000. Total = 5! = 120.
Grand total = 48 + 120 = 168.
4-digit numbers > 7000: The thousands digit must be 7, 8 (digits ≥ 7 from the set). That gives 2 choices for the first digit, then 4×3×2 = 24 arrangements for the remaining 3 digits. Total: 2 × 24 = 48.
5-digit numbers: All 5-digit numbers using 3,5,6,7,8 without repetition are automatically > 7000. Total = 5! = 120.
Grand total = 48 + 120 = 168.
[JEE Main 2023 · 24 Jan · Shift 2]