The number of integers greater than 6000 that can be formed using the digits 3, 5, 6, 7 and 8 without repetition is
- A.216
- B.192
- C.120
- D.72
Show answer and solution
Correct option: B
Solution
Numbers greater than 6000 can be 4-digit or 5-digit.
5-digit numbers: All arrangements of {3,5,6,7,8} = 5! = 120.
4-digit numbers: First digit must be 6, 7, or 8 (3 choices) to ensure the number > 6000. Remaining 3 digits from the 4 left = 4×3×2 = 24 arrangements. Total = 3×24 = 72.
Grand total = 120 + 72 = 192.
5-digit numbers: All arrangements of {3,5,6,7,8} = 5! = 120.
4-digit numbers: First digit must be 6, 7, or 8 (3 choices) to ensure the number > 6000. Remaining 3 digits from the 4 left = 4×3×2 = 24 arrangements. Total = 3×24 = 72.
Grand total = 120 + 72 = 192.
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