Question:
How many numbers (without repetition) between \(400\) and \(1000\) can be made with the digits \(2,3,4,5,6,\) and \(0\)?
How many numbers (without repetition) between \(400\) and \(1000\) can be made with the digits \(2,3,4,5,6,\) and \(0\)?
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The numbers are three-digit with hundreds digit 4, 5 or 6.
Updated On: Nov 12, 2026
- \(120\)
- \(720\)
- \(60\)
- \(24\)
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Verified By Collegedunia
The Correct Option is C
Solution and Explanation
Step 1: Understanding the Concept
Numbers between 400 and 1000 are three-digit numbers with hundreds digit at least 4.
Step 2: Hundreds place
From digits 2, 3, 4, 5, 6, 0 the hundreds digit can be 4, 5 or 6, so 3 choices.
Step 3: Remaining places
The tens digit has 5 choices and the units digit has 4 choices (no repetition).
Step 4: Multiply
Total \(=3\times5\times4=60\)
Final Answer:
There are 60 such numbers. \[ \boxed{\text{(C) }60} \]
Numbers between 400 and 1000 are three-digit numbers with hundreds digit at least 4.
Step 2: Hundreds place
From digits 2, 3, 4, 5, 6, 0 the hundreds digit can be 4, 5 or 6, so 3 choices.
Step 3: Remaining places
The tens digit has 5 choices and the units digit has 4 choices (no repetition).
Step 4: Multiply
Total \(=3\times5\times4=60\)
Final Answer:
There are 60 such numbers. \[ \boxed{\text{(C) }60} \]
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