Question:
Let \( A = \{0,2,4,6,8\} \). The number of 5-digit numbers that can be formed using the digits in \( A \) without replacement, is
Let \( A = \{0,2,4,6,8\} \). The number of 5-digit numbers that can be formed using the digits in \( A \) without replacement, is
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For number formation, always subtract cases where leading digit is zero.
Updated On: Apr 21, 2026
- \(120 \)
- \(96 \)
- \(88 \)
- \(64 \)
- \(32 \)
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The Correct Option is B
Solution and Explanation
Concept:
First digit of a number cannot be zero.
Step 1: Total permutations.
\[ \text{Total ways} = 5! = 120 \]
Step 2: Subtract invalid cases (starting with 0).
Fix 0 at first place, arrange remaining 4 digits: \[ 4! = 24 \]
Step 3: Valid numbers.
\[ 120 - 24 = 96 \]
Step 1: Total permutations.
\[ \text{Total ways} = 5! = 120 \]
Step 2: Subtract invalid cases (starting with 0).
Fix 0 at first place, arrange remaining 4 digits: \[ 4! = 24 \]
Step 3: Valid numbers.
\[ 120 - 24 = 96 \]
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