Hi! I have tried to figure out these problems so many times and each time my brain almost explodes. The book doesn't explain what (!) is, it just shows a high answer and I'm completely lost. So any help would be appreciated. Thanks!

1) The first problem is "How many different permutations can you make with the letters in the word s e v e n t e e n?" So far I've gotten to : 9! / (4! x 2!). not knowing what (!) is has me stuck.

2) In how many ways can you fill three different positions by choosing from 15 different people? (This question is for confirmation of my answer, 15 x 14 x 13)

3) A teacher has a set of 12 problems to use on a math exam. The teacher makes different versions of the exam by putting 10 questions on each exam. How many different exams can the teacher make?

4) Car thieves steal one automobile out of 400 of a certain type every year in a certain city. What annual net premium should an owner pay for theft insurance in the amount of $16,000 on the certain type of car?(Another confirmation for my answer, $400)

5) Suppose you draw a card from a well-shuffled pack of playing cards. What is the probability the card you draw will be an ace? (And once more another confirmation for my answer, 1/ 52)

6) In how many ways can you arrange eight books on a shelf?

Thanks so much again! If this is too much can you just explain the first few to me so I can figure out the rest. Thanks!