Question

The number of all four-digit numbers which begin with 4 and end with either zero or five is

• A. \( 200 \)
• B. \( 64 \)
• C. \( 256 \)
• D. \( 32 \)

Hint:

When calculating the total number of possibilities for a number with fixed digits, simply multiply the number of choices for each free position.

Answer 1

The Correct Option is A

We are tasked with constructing a four-digit number that starts with \( 4 \) and ends with either \( 0 \) or \( 5 \). In this case, the first and last digits are fixed, while the middle digits can vary.
The first digit is fixed as \( 4 \), so there is only one choice for it.
The second and third digits can each be any digit from \( 0 \) to \( 9 \), providing 10 choices for each.
The last digit has two possible values: \( 0 \) or \( 5 \), giving us 2 choices.
To determine the total number of valid four-digit numbers, we multiply the number of choices for each digit: \[ 1 \times 10 \times 10 \times 2 = 200. \] Final Answer: \[ \boxed{200} \]