Question

A four character password consists of one letter from the word MATH followed by three digits which may be 1 2 or 3. If the digits may be used more than once, how many more passwords can be made if the numbers are only used once? 12,24,84,108 and if you know the answer how the heck did you figure it out

Answer 1

what do you mean by characters?

Answer 2

It would be 4 *3!=24. There are 4 ways of selecting a letter and there are 3! ways of permuting the 3 digits

Answer 3

Well, first, you figure out how many possibilities there are if they can be used more than once, and then how many possibilities if the numbers aren't repeated. Respectively,\[4*3^3 - 4*3! = 84\]

Answer 4

And king george you're supposed to find the number of ways to fill it with digits not repeated not the other way round.

Answer 5

In my formula, the \(4*3^3\) comes from 4 possible letters, then every number can be chosen 3 times, and there are 3 digits to choose from. Meanwhile, the \(4*3!\) is derived from the fact that there are 4 possible letters, but since you can't repeat numbers, you have three choices for the first number, two choices for the second, and one for the last. Thus, \(4*3^3 - 4*3! = 84\) is your desired answer

Answer 6

King geroge:108-84=24. is the answer you have found the opposite case.You're supposed to use the digits only once. Not find the ways in which the digits can be used more than once.

Answer 7

I'm either not reading the question correctly then, or misunderstanding it, since you can make more passwords if the numbers can be repeated.

Answer 8

" If the digits may be used more than once, how many more passwords can be made if the numbers are only used once? " Hmmm. I agree it seems a bit ambiguous.