how many 3 digit numbers can be formed using the digits 0,1,2,3,4,5,6, if repitition is not allowed?

assuming no leading zeros, there would be

6 * 6 * 5

candidates.

Since starting with 0 would not make it a 3-digit number, we have only 6 choices for the lead digit

so number of cases
= 6 x 6 x 5
= 180

To find out how many 3-digit numbers can be formed using the digits 0, 1, 2, 3, 4, 5, and 6 without repetition, we can use the concept of permutations.

The first digit of a 3-digit number can be chosen from the given digits in 7 ways (0, 1, 2, 3, 4, 5, or 6).

Once the first digit is chosen, there are 6 remaining digits left for the second digit. Hence, the second digit can be chosen in 6 ways.

Similarly, after choosing the first two digits, there will be 5 remaining digits for the third digit. Hence, the third digit can be chosen in 5 ways.

Therefore, the total number of 3-digit numbers without repetition can be calculated as:

7 * 6 * 5 = 210

So, there are a total of 210 different 3-digit numbers that can be formed using the given digits without repetition.