How many 4 digit numbers greater than or equal to 3000 and less then 8000 can be formed with no repition in there digits??
the first digit has to be either a 4,5,6, or 7
number of cases
= 4 x 9 x 8 x 7
= 2016
I have a multiple choice answer of 5000, 5040, 120 or 2520??
According to your wording, a digit cannot be used more than once.
I stand by my answer .
reiny,the first digit can also be 3..read the question again
To find the number of 4-digit numbers greater than or equal to 3000 and less than 8000, with no repetition of digits, we can use the concept of permutations.
The first digit can be chosen from the set {3, 4, 5, 6, 7}. Let's call this the thousands digit.
Since there are no repetitions, there are 5 options for the thousands digit.
The second digit can be chosen from the set of all digits (0-9) excluding the digit used for the thousands place.
Since there are no repetitions, there are 9 options for the hundreds digit.
Similarly, the tens digit can be chosen from the set of all digits (0-9) excluding the digits used for the thousands and hundreds places.
Again, there are no repetitions, so there are 8 options for the tens digit.
Finally, the units digit can be chosen from the set of all digits (0-9) excluding the digits used for the thousands, hundreds, and tens places.
For the units digit, we have 7 options.
Using the fundamental principle of counting, we multiply the number of choices together:
5 (for thousands digit) × 9 (for hundreds digit) × 8 (for tens digit) × 7 (for units digit) = 2,520.
Therefore, there are 2,520 4-digit numbers, greater than or equal to 3000 and less than 8000, that can be formed with no repetition in their digits.