a password consists of 6 lowercase letters, how many passwords are possible if the letter a appears exactly once

Question

rizags · Answer

$$_ _ _ _ _ _  with 26 possibilities correct?$$

anonymous · Answer

yes, but you must use the letter 'a' exactly once

rizags · Answer

what about the other letters. Can they appear as many times as possible? can you have abbbbb?

anonymous · Answer

yes you are allowed to do that

rizags · Answer

assuming that for the other five letters, repetition is allowed, the scenario is as follows:

rizags · Answer

$$\left( 1\times25\times25\times25\times25\times25 \right)\times6$$

anonymous · Answer

ahh yes that is the correct answer! 
 could you please give a short explanation

rizags · Answer

sooo, for the first spot, we have only one choice: a. For the next five spots, we have 25 choices: b through z. HOWEVER, there are six cases for this, because there are six positions for a. therefore the answer is $$25^{5}\times6$$

rizags · Answer

make sense?

anonymous · Answer

actually, i think i understand it now, you have to use the fundamental principle of counting

rizags · Answer

kind of, yes

anonymous · Answer

okay, thanks for your help!

rizags · Answer

yep! medal and friend plzzzz lol