Question

The letters a, e, i, o, u, and y are used to form 6-letter passwords for a movie theater security system. How many passwords can be formed if the letters can be used more than once in any given password?

Answer 1

Since each letter can be used more than once in any given password, we can use the multiplication rule to find the total number of possible passwords.

There are 6 positions in the password, and each position can be filled with any of the 6 letters (a, e, i, o, u, y). Therefore, the total number of possible passwords is:

6 x 6 x 6 x 6 x 6 x 6 = 46656

So there are 46,656 possible passwords that can be formed if the letters can be used more than once in any given password.

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