My friend and I are discussing a question on permutations.

A grid of 49 letters, numbers and symbols is shown. A random character is taken from the grid. This is done six times. The idea is for this to randomly generate a password. What are the total number of passwords that could be generated?

My thought is that there is a 1/49 chance of any character being chosen, therefore the total number of passwords is 49^6.

My friend says that because this is a permutations question, the formula for permutations makes it (49!)/(49-6)!

However I'm pretty sure this is when you have the "balls in a sack" type question, and each time you take a ball out of the sack you don't return it, so it doesn't apply in this case as a valid password could be "111111" (i.e. the same character repeated each time).

Our problem is that the question is assigned 10 points, and that so far we can't find any similar examples in the course material of how they want the question answered. My friend points out that you don't get a 10 point question whose answer is 49^6.

So I'd appreciate some feedback - who is right in solving the problem? Any suggestions what working to include in order to get all 10 of those points??

Also I would strongly suggest that you look at how the question is worded. It's not clear to me from your description if the letter is "returned" to the rack after it is selected or if it then becomes unavailable. eg, the letter X can only occur ONCE in the password or can it occur multiple times.

Good luck.