# What is the number of passwords can be made under this restriction?

I'm facing difficulties while solving this problem: A password contains 5 digit numbers and 5 small english letters. how many possible passwords can be made?

If I solve it like this: 26^5 x 10^5 this will not count passwords that are mixed and digit-first passwords.

• You're right that $26^5 10^5$ is the number of passwords that match the pattern LLLLLNNNNN. How many patterns are possible?
– Karl
Jan 1 at 23:51
• @Karl Each password must have 5 digits and 5 letters. Other than this there are no more restrictions. So any pattern that has 5 digits and 5 letters, is allowed. Jan 2 at 0:00
• How many ways are there of choosing $~5~$ positions out of $~10,~$ sampling without replacement, where order of selection is regarded as unimportant? The $~5~$ selected positions can be regarded as the positions that the digits will occupy, with the letters going in the remaining positions. Jan 2 at 0:04
• @user2661923 Is this a question or what? In mine the order is important and it is with replacement/repetition Jan 2 at 0:09
• I don't know what else to say. Is this an assigned problem from a math course? Perhaps you could ask your teacher for help, or ask the school if a tutor is available? Jan 2 at 0:36

• not exactly $2^{10}$ since everytime a digit or letter is used the chances of the next draw get affected it is not $50|50$ anymore. This means the positions of letters and digits are being chosen "without replacement". Jan 2 at 1:14
• Lets put an $L$ in every position that's fixed for a letter. You are trying to figure out how many different positions the five $L$s can take out of $10$ possible positions. Jan 2 at 1:58