How many numbers less than 10000 can be formed by using digits 1,2,3,0,4,5,6,7 ?
To determine how many numbers can be formed using the given digits, we need to consider the positions of the digits in the number.
In this case, since the number should be less than 10000, it is a four-digit number. Let's consider the positions of the digits from left to right: thousands, hundreds, tens, and units.
To find how many numbers can be formed using the given digits, we can analyze each position:
1. Thousands Digit:
Since the number should be less than 10000, the thousands digit can only be one of the digits 1, 2, 3, or 0. So, there are 4 possibilities for the thousands digit.
2. Hundreds, Tens, and Units Digits:
The remaining digits (4, 5, 6, 7) can be placed in the hundreds, tens, and units positions.
We have four choices for each of these three positions (repetition is allowed). Thus, there are 4 options for the hundreds digit, 4 options for the tens digit, and 4 options for the units digit.
To find the total number of possible numbers, we multiply the number of options for each position together:
Total = (number of options for thousands digit) * (number of options for hundreds digit) * (number of options for tens digit) * (number of options for units digit)
Total = 4 * 4 * 4 * 4 = 256
So, there are 256 numbers less than 10000 that can be formed using the given digits.