How many numbers between 300 and 800 can be made by using digits 2,4,5,6 and 0?Choices:- 36 72 144 180

To solve this problem, we need to consider the conditions given:

1. The number must be between 300 and 800.
2. We can use the digits 2, 4, 5, 6, and 0.

Given these conditions, we can break down the problem into three cases based on the hundreds digit:

1. If the hundreds digit is 3, we have no choice because only 3 is in the range of 300 to 800. The tens digit can be any of the 4 remaining digits (2, 4, 5, 6), and the units digit can be any of the 5 given digits (2, 4, 5, 6, 0). So, we have 145 = 20 numbers in this case.

2. If the hundreds digit is 4, 5, or 6, we have 3 choices. The tens digit can be any of the 4 remaining digits (including 0), and the units digit can be any of the 5 given digits. So, we have 345 = 60 numbers in this case.

3. If the hundreds digit is 7 or 8, we have no valid numbers because we can't use the digits 7 or 8.

So, adding up the numbers from the two valid cases, we have 20 + 60 = 80 numbers that can be made using the digits 2, 4, 5, 6, and 0 between 300 and 800.

Therefore, none of the given choices (36, 72, 144, 180) is correct. The correct answer should be 80.