Question

Number of three digit numbers that can be formed using 0, 1, 2, 3, and 5 where these digits are allowed to repeat any number of times, is equal to:

• A. 125
• B. 100
• C. 115
• D. 140

Hint:

When forming numbers with restrictions, carefully consider the choices for each digit based on its position.

Answer 1

The Correct Option is B

To form a three-digit number, we have three places to fill: hundreds, tens, and ones. The possible digits are 0, 1, 2, 3, and 5, but the first digit (hundreds place) cannot be 0 (since it is a three-digit number). So, we analyze the choices for each place:

Step 1: Hundreds Place.
The hundreds place can be filled by any digit except 0, so we have the choices 1, 2, 3, or 5. Hence, there are 4 choices for the hundreds place.

Step 2: Tens Place.
The tens place can be filled by any of the 5 digits (0, 1, 2, 3, 5), so there are 5 choices for the tens place.

Step 3: Ones Place.
The ones place can also be filled by any of the 5 digits (0, 1, 2, 3, 5), so there are 5 choices for the ones place.

Step 4: Total Combinations.
The total number of three-digit numbers that can be formed is the product of the number of choices for each place: \[ 4 \times 5 \times 5 = 100. \] Thus, the number of such three-digit numbers is 100.