counting principle problems

1. in a volleybal team, there are 12 members, one coach, and 2 managers. In how many ways can 7 kneel for a team picture?
2. Julia can choose one of 3 buses or take one of 2 trains and then walk using one of the 4 routes to her work. In how many ways can she get to work?
3. In California, license plates must follow this pattern: one digit, three letters, and three digits. (ex. 1ABC345). Find the total number of license plates if: the first digit cannot be zero and the three letters cannot form the word "GOD"
4. A locker has a 5-digit combination. Find the total number of combinations if: the first digit cannot be zero and there cannot be 5 consecutive 5s.

afrazer721 said:

which is equal to 9*10*10*10*10*9. I not sure if this is correct but that's how I interpret the question.

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afrazer721 said:

Problem #2 is a combination formula:
one bus at random from a group of three buses in any order is 3!/(3-1)!1!=3
one train at random from a group of two trains in any order is 2!/(2-1)!1!=2
one route at random from a group of four routes in any order is 4!/(4-1)!1!=4
3*2*4=24=the many ways she can get to work.

Problem # 3 is a permutation formula:
The first digit can be any one of nine digits and the remaining three can be chosen which is
10P3=10!/(10-3)!.
You want the number of ways of not choosing three letters from the full alphabet(26) because you don't want to arrange the letters into the word, 'GOD' which is 26P3=26!/(26-3)!.
So, 9*(10!/(10-3)!)*(26!/(26-3)!)=total # of license plates.

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