Hello,

I'm not too sure what the formal name for these problems is (my professor calls it the $\displaystyle $ C^{m}_{n} $$ 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...

4 "A"s?

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.