# Math Help - [SOLVED] How many six-letter computer passwords are possible?

1. ## [SOLVED] How many six-letter computer passwords are possible?

If upper-case and lower-case letters are considered as different letters,how many six-letter computer passwords are possible
a) with no repeated letters?
b) with at least one capital letters?

1)19 770 609 664
2)19 461 693 888

Would anyone be able to help me with this question?

2. ## Combinations and Permutations

Hello, this is a problem involving combinations and permutations, now because it involves the arrangement of 6 letter words, we use the permutative formula

nPr = n!/(n-r)!

Or in other words, how many different combinations from 52 letters can 6 letter words be made?

If this doesn't help message back.

3. Originally Posted by andrew2322
Hello, this is a problem involving combinations and permutations, now because it involves the arrangement of 6 letter words, we use the permutative formula

nPr = n!/(n-r)!

Or in other words, how many different combinations from 52 letters can 6 letter words be made?

If this doesn't help message back.
That answers part (a) (and the answer the OP gives for part (a) is actually wrong - it's the answer for repetition being allowed).

Part (b) requires clarification on whether or not repetition is allowed. The answer given by the OP is consistent with repetition being allowed: $52^6 - 26^6$.

All this is moot since the OP asked this question at another website and got a correct response. Which is why I marked the thread as Solved. I probably should have closed the thread as well but I thought there might have been some fresh insight ....