126, hmm, seems a bit low at first glance. however, when you think about it, it really does seem about right, because I never mentioned what order they have to come it, just the combinations.
Schmoe: Your value of 126 looks correct to me. My analysis had an error which you identified. BTW: How often do posters acknowledge having made an error?
Didn't anyone besides one person make it beyond basic math? There are five distinct choices and you buy a combination of five. Therefore, for the first one you have five choices, and for the second (and so on) you have five choices. So it's simply 5x5x5x5x5 or 5^5 as was stated earlier. No more, no less.
Light: If you number the types 1 through 5 and order one of each, your order can be described as 12345, 54321, 13524, et cetera. When dealing with decimal notation, there is an obvious difference between 12345 and 54321. When using the digits as codes for types of sandwiches, there is no difference between 12345 and 543421. I think Smhoe posted a comment similar to the above. Your 5<sup>5</sup> formula is correct for the number of decimal numbers that can be expressed using the digits 1-5 with repetition of digits allowed.
