counting: 26 types of letters in 12 bit string. Must begin with ST and have three T's

I have a counting problem.

I have 26 types of letters in 12 bit string. It must begin with ST and have three T's in the string.

How to solve this ??

I also have this problem.

A pizzaplace has 3 sizes of pizza's, 2 types of crust, filled and not filled and 12 types of toppings.

How many types of pizza can I make. I can also have pizza with nothing.

Re: counting: 26 types of letters in 12 bit string. Must begin with ST and have three

Hey frimanns.

For the first one (assuming you can only have an S and a T), you fix the first two which gives ten digits that can vary. If you have 10 digits with two possibilities, this gives 2^10 = 1024 possibilities.

Now if you three T's in the string as a whole then you include the T in the "ST" and you need exactly two more T characters. So you need to find the number of ways of choosing 2 T's from 10 available slots. Have you done this in your class yet?

If you haven't done this, then explain what kind of things you have done and how your teacher explained it.