If a three digit number id formed from the digits 1, 2, 3, 4, 5, 6, and 7 with no repetitions, tell how many of this three digit numbers will have a number value between 100 and 500.

If it starts with a 1, 2, 3, or 4:

4 choices for the first number
6 choices for the second number
5 choices for the third number

If it starts with a 5:
1 choice for the first number
1 choice for the second number
1 choice for the third number

Therefore,
4*6*5 + 1*1*1 = 121

Correction: it can't start with a 5 as there are no zeroes to choose.

So just 4*6*5 = 120

To find the number of three-digit numbers that can be formed using the digits 1, 2, 3, 4, 5, 6, and 7 with no repetitions and have a value between 100 and 500, we can break it down into three cases:

Case 1: The first digit is 1.
In this case, the second digit can be any of the remaining six digits (2, 3, 4, 5, 6, or 7), and the third digit can be any of the remaining five digits. So, there are 6 choices for the second digit and 5 choices for the third digit. Therefore, there are 6 * 5 = 30 three-digit numbers that can be formed in this case.

Case 2: The first digit is 2.
Similar to Case 1, the second digit can be any of the remaining six digits, and the third digit can be any of the remaining five digits. So, there are again 6 choices for the second digit and 5 choices for the third digit. Therefore, there are 6 * 5 = 30 three-digit numbers that can be formed in this case.

Case 3: The first digit is 3 or 4.
In this case, the second digit can be any of the remaining five digits (2, 3, 4, 5, or 6), and the third digit can be any of the remaining five digits. So, there are 5 choices for both the second and third digits. Therefore, there are 5 * 5 = 25 three-digit numbers that can be formed in this case.

Now, to find the total number of three-digit numbers that have a value between 100 and 500, we add up the numbers from all three cases: 30 + 30 + 25 = 85.

So, there are 85 three-digit numbers that can be formed using the digits 1, 2, 3, 4, 5, 6, and 7 with no repetitions and have a value between 100 and 500.