consider determining how many possible phone numbers are in an area code (repeated numbers allowed)

is this a combination, permutation or neither....

my answer neither

combination.

combination.

wouldn't it be neither because we are allowed to use repeated numbers....therefore it can't be combination or permutaition

You are correct, the concept of combination or permutation is not applicable in this case because repeated numbers are allowed.

In a combination, the order of the elements does not matter, and repetitions are not allowed. For example, if there are only three available digits (0, 1, and 2), the combination of those digits would be {0,1}, {0,2}, and {1,2}.

In a permutation, the order of the elements matters, but repetitions are not allowed. Using the same example, the permutations would be {0,1}, {1,0}, {0,2}, {2,0}, {1,2}, and {2,1}.

In the case of determining how many possible phone numbers are in an area code with repeated numbers allowed, we need to consider each digit of the phone number independently. Since repetitions are allowed, each digit has 10 possible choices (0-9). Therefore, the total number of possible phone numbers in an area code can be calculated by multiplying the number of choices for each digit.

For example, if a phone number consists of 7 digits, the total number of possible phone numbers in that area code would be 10^7, which equals 10,000,000.

So, in this case, it is neither a combination nor a permutation but rather a simple calculation of the number of choices for each digit.