Question

How many 5-digit numbers are there with distinct digits?

• A. 144
• B. 27216
• C. 4386
• D. 6432
• E. 720

Hint:

Distinct-digit numbers ke liye pehle leading digit constraints handle karo (zero nahi ho sakta), phir baaki positions ke liye decreasing choices multiply karo.

Answer 1

The Correct Option is B

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:
\[ \boxed{27216} \]