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.

Answer 1

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

Answer 2

Correction: it can't start with a 5 as there are no zeroes to choose.
So just 4*6*5 = 120