 # I am to create a six character password that consists of 2 lowercase letters and 4 numbers. The lett kulisamilhh 2022-05-03 Answered
I am to create a six character password that consists of 2 lowercase letters and 4 numbers. The letters and numbers can be mixed up in any order and I can also repeat the same number and letter as well. How many possible passwords are there?
What I have pieced together so far:
Well, from the fundamental counting principle, we would definitely need ${26}^{2}×{10}^{4}$ but obviously this is not all the possibilities since I can rearrange letters and numbers. Since it is a password the order matters so would I try and do a permuation of some sort like ${}^{6}{P}_{2}$ since there are 6 slots to try to rearrange 2 objects (letters)?
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You're just a little wrong on the letters-numbers arrangement part; it's $\left(\genfrac{}{}{0}{}{6}{2}\right)=15$, not ${}^{6}{P}_{2}=30$ (since we do the arrangement before the character assignment).
Now multiply this with your (correct) value of ${26}^{2}×{10}^{4}$ character assignments to get the final answer: ${26}^{2}×{10}^{4}×\left(\genfrac{}{}{0}{}{6}{2}\right)$.