Question:
The number of integers greater than 6000 that can be formed by using the digits 0, 5, 6, 7, 8 and 9 without repetition is
The number of integers greater than 6000 that can be formed by using the digits 0, 5, 6, 7, 8 and 9 without repetition is
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When counting numbers with digit restrictions, handle digit placement constraints (like starting digits) carefully and use permutation formulas.
Updated On: Jun 6, 2025
- 240
- 840
- 1440
- 1680
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The Correct Option is C
Solution and Explanation
Form 4-digit numbers $>6000$ using digits {0,5,6,7,8,9} without repetition. The first digit must be 6,7,8,9 (4 choices), remaining digits from rest (5P3 = 60).
Total = $4 \times 60 = 240$
Similarly, count 5-digit and 6-digit numbers formed from remaining digits (6P5 = 720, 6P6 = 720), add all: $240 + 720 + 480 = 1440$
Total = $4 \times 60 = 240$
Similarly, count 5-digit and 6-digit numbers formed from remaining digits (6P5 = 720, 6P6 = 720), add all: $240 + 720 + 480 = 1440$
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