1. ## Combinatorial Probability

I have a question about one of the parts of an exercise in a text on Probability and Statistics, particularly why the answer to (b) is $16!$.

Exercise 1-11 An engineering faculty shuffles the quizzes of his 17 students and redistributes them randomly for peer grading.

(a) In how many different ways may the quizzes be handed out?
(b) In how many ways may Kendra, one of the 17 students, be assigned her own quiz for grading?
(c) What is the probability that Kendra will receive her own quiz?

(a) The different ways 17 quizzes may be handed out to 17 students is simply the number of distinct ways of rearranging all 17 quizzes, or $_{17}P_{17} = 17!$.

(b) The solutions manual says the answer is $16!$ but I don't know why it isn't $_{17}P_{1}$.

(c) I know it's the answer to (a) divided by the answer to (b), but I don't know why the answer to (b) is $16!$.

2. If I give you your own quiz, then how many can I pass out the other quizzes?