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:Understand the condition for divisibility by 10.
A number is divisible by 10 if its last digit is 0. Therefore, in this case, we need to place 0 in the units place.
Step 2:Select the remaining digits.
The remaining digits are 1, 2, 3, 4, and 5. We need to form a five-digit number with these digits, using one of the remaining four digits for each place (tens, hundreds, thousands, and ten-thousands).
Step 3:Number of ways to form the number.
- The units digit is fixed as 0.
- For the ten-thousands place, we can choose any of the remaining 5 digits (1, 2, 3, 4, or 5), so there are 5 choices.
- For the thousands place, we can choose any of the remaining 4 digits (after selecting the ten-thousands digit), so there are 4 choices.
- For the hundreds place, we can choose from the remaining 3 digits, so there are 3 choices.
- For the tens place, we can choose from the remaining 2 digits, so there are 2 choices. Thus, the total number of such numbers is: \[ 5 \times 4 \times 3 \times 2 = 120 \]
Step 4:Final Answer.
Therefore, the number of five-digit numbers that are divisible by 10 is 120.