I'm not too sure what the formal name for these problems is (my professor calls it the formula). I am having trouble finding answers, though, as I get different ones each time (I'm fine with permutations and combinations, though). Here the problems:
1) I have a 7 digit password made up of 3 numbers (1 - 9) and 4 letters (A - Z). How many passwords are there with...
at least 2 "A"s
three numbers next to each other
four letters next to each other
no two letters next to each other
2) A bag of chips has 10 chips in it: 1 sour cream and onion, 2 BBQ, 3 regular, and 4 low fat chips. I pick 5 chips at random. How many picks are there with...
at lest 2 BBQ chips
at least 2 BBQ chips and 1 regular chip
all 4 chips represented
at most 3 chips represented
at least 2 chips represented
Let me know if I should show my (erroneous) work or not.