Can you please check my work and help me with the parts that I don't understand?

Question

For each event, choose the most appropriate term and solve the problem.

1. In a sweepstakes with nine hundred entries, the first winner selected receives the grand prize, the second receives first prize, and so on until all thirty prizes are awarded. How many possible outcomes are there?
900^ P 30

Counting Principle, combination, factorial, or permutation

I chose permutation- My work: 900!/(900 - 30) = 900!/870!.. From here, do I simplify?

2. Six friends go to a movie. How many ways can they sit in a row of six seats?
Counting Principle, combination, factorial, or permutation. I chose permutation
My work: 6x5x4x3x2x1 = 720 ways

3.Of the fifty states, five are randomly selected to have their governor participate in a summit. How many different groups of governors can go? 50!/(50 - 5)!.5!

Counting Principle, combination, factorial, or permutation

I chose combination- I'm really not sure how to solve this.

Thank you so much for your help!

Answer 1

#1 correct. 900P30 is the simplest possible answer. Trying to evaluate it does not add much to understanding the value of the answer. Suffice it to say that 2.6*10^88 is pretty big.

#2 ok

#3 ok 50C5 - combinations, since the order of their selection does not matter.

Answer 2

Thanks :)

Answer 3

If Jeremy has 17 chocolate bars and he give 3 to Lucy and gets 5 from Bruno, how many chocolate bars does Jeremy have now? All of my friends say "diabetes" but I have repeatedly told them that diabetes is not a number but they stick with it. I believe that Jeremy has 19 chocolate bars left and that's what they wrote down (my friends)but they said it was just to trick cheaters. I for one, believe that the answer is 19.