Question

The number of five digits numbers that can be formed without any restriction is

• A. 990000
• B. 10000
• C. 90000
• D. None of these

Hint:

First digit cannot be 0 for a five-digit number.

Answer 1

The Correct Option is C

The problem asks for the number of five-digit numbers that can be formed without any restrictions. Let's break down the requirements of a five-digit number:

• A five-digit number cannot start with zero.
• It must have exactly five digits.

We will calculate the number of such five-digit numbers step-by-step:

1. Determine the choices for the first digit: Since the number cannot start with zero, the first digit has 9 possibilities (1 to 9).
2. Determine the choices for the other four digits: Each of the remaining four digits can be any digit from 0 to 9, providing 10 choices per digit.
3. Calculate the total number of five-digit numbers: The total number is calculated by multiplying the number of choices for each digit position.

The formula used here is:

Total number of five-digit numbers	=	Number of choices for the first digit × Number of choices for each of the other four digits
	=	\(9 \times 10 \times 10 \times 10 \times 10\)

Calculating this, we get:

• \(9 \times 10^4 = 9 \times 10000 = 90000\)

Thus, the correct answer is 90000.

Option 3 (90000) is the correct answer, as it matches our calculated result. Other options either provide the incorrect number of total possibilities or are not plausible given the constraints.