Question

Five digit number is formed using the digits 0, 1, 2, 3, 4, and 5 without repetitions. Number of five digit numbers which are divisible by 10 is:

• A. 360
• B. 240
• C. 120
• D. 480
• E. 520

Hint:

For a number to be divisible by 10, its last digit must be 0. The rest of the digits can be selected and arranged in any order.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept
For a number to be divisible by 10, its last digit (units place) must be 0. Since we are forming a 5-digit number without repetition, once 0 is fixed at the end, we arrange the remaining digits in the other places.
Step 2: Detailed Calculation
1. Digits available: {0, 1, 2, 3, 4, 5} (Total 6 digits). 2. Constraint (Divisibility by 10): The units place is fixed with the digit '0'. (1 way) 3. Filling the remaining 4 places: - We need to choose and arrange 4 digits from the remaining 5 digits {1, 2, 3, 4, 5}. - The number of ways to fill the 1st place: 5 options. - The number of ways to fill the 2nd place: 4 options. - The number of ways to fill the 3rd place: 3 options. - The number of ways to fill the 4th place: 2 options. 4. Total Numbers: $5 \times 4 \times 3 \times 2 \times 1 = 120$.
Step 3: Final Answer
The number of five-digit numbers divisible by 10 is 120.