Question:
How many 5-digit numbers are there with distinct digits?
How many 5-digit numbers are there with distinct digits?
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Distinct-digit numbers ke liye pehle leading digit constraints handle karo (zero nahi ho sakta), phir baaki positions ke liye decreasing choices multiply karo.
Updated On: Sep 30, 2025
- 144
- 27216
- 4386
- 6432
- 720
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Verified By Collegedunia
The Correct Option is B
Solution and Explanation
Step 1: Leading digit cannot be zero.
First digit (ten-thousands place) has \(9\) options: \(1\) to \(9\).
Step 2: Remaining digits must be distinct, zero allowed now.
After fixing the first digit, remaining available digits \(= 9\).
Thus subsequent places have: \(9, 8, 7, 6\) options respectively.
Step 3: Multiply the choices (Multiplication Principle).
Total \(= 9 \times 9 \times 8 \times 7 \times 6\).
Compute: \(9 \times 9 = 81\), \(81 \times 8 = 648\), \(648 \times 7 = 4536\), \(4536 \times 6 = 27216\).
Final Answer:
\[ \boxed{27216} \]
First digit (ten-thousands place) has \(9\) options: \(1\) to \(9\).
Step 2: Remaining digits must be distinct, zero allowed now.
After fixing the first digit, remaining available digits \(= 9\).
Thus subsequent places have: \(9, 8, 7, 6\) options respectively.
Step 3: Multiply the choices (Multiplication Principle).
Total \(= 9 \times 9 \times 8 \times 7 \times 6\).
Compute: \(9 \times 9 = 81\), \(81 \times 8 = 648\), \(648 \times 7 = 4536\), \(4536 \times 6 = 27216\).
Final Answer:
\[ \boxed{27216} \]
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