How many numbers less than 500 can be formed using the digits 12345 and 6 without repetitions?

Answer 1

To determine the number of numbers that can be formed using the digits 1, 2, 3, 4, 5, and 6 without repetitions and less than 500, we first consider the hundreds place. Since the number has to be less than 500, the hundreds place can only be filled with 1, 2, or 3. For the tens and units place, any of the remaining digits can be used. Therefore, there are 3 choices for the hundreds place, 4 choices for the tens place, and 3 choices for the units place, giving a total of 3 x 4 x 3 = 36 numbers that can be formed.

Answer 2

There is no limitation given to the number of digits in the number, thus:

For 3 digit numbers: to be less than 500 the first digit can be only one of {1, 2, 3, 4} leading to 4 × 5 × 4 = 80 numbers

For 2 digit numbers: they are all less than 500, and there are 6 × 5 = 30 numbers

For 1 digit numbers: they are all less than 500, and there are 6 numbers

Thus there are in total 80 + 30 + 6 = 116 numbers that can be made form the digits {1, 2, 3, 4, 5 ,6} without repetitions that are less than 500.