Question:
The number of integers greater than 7000 using 2, 4, 6, 7, 8 without repetition is ________.
The number of integers greater than 7000 using 2, 4, 6, 7, 8 without repetition is ________.
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Don't forget to count numbers with more digits than the lower bound.
Updated On: Jun 26, 2026
- 168
- 336
- 196
- 256
- 512
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The Correct Option is A
Solution and Explanation
Step 1: Concept
Count 4-digit numbers $> 7000$ and all 5-digit numbers.
Step 2: Meaning
Available digits: $\{2, 4, 6, 7, 8\}$ (5 digits).
Step 3: Analysis
4-digit numbers starting with 7 or 8: $2 \times 4 \times 3 \times 2 = 48$. 5-digit numbers: $5 \times 4 \times 3 \times 2 \times 1 = 120$.
Step 4: Conclusion
Total integers $= 48 + 120 = 168$. Final Answer: (A)
Count 4-digit numbers $> 7000$ and all 5-digit numbers.
Step 2: Meaning
Available digits: $\{2, 4, 6, 7, 8\}$ (5 digits).
Step 3: Analysis
4-digit numbers starting with 7 or 8: $2 \times 4 \times 3 \times 2 = 48$. 5-digit numbers: $5 \times 4 \times 3 \times 2 \times 1 = 120$.
Step 4: Conclusion
Total integers $= 48 + 120 = 168$. Final Answer: (A)
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