Combinations, Permutations and Probability

Question

You have acquired 10 music CDs over the past 12 months. You put them in a portable CD caddy that holds exactly 10.

(a) How many arrangements are possible in
the caddy?
(b) Suppose I try to guess your top 5 favorite
CDs. How many possible guesses do I
have?
(c) What is the probability I can do that on the
first try?

Answer 1

a) I believe that since there is no particular order, that the answer is 10!.  The first CD has 10 placement options, the second CD has 9, the third CD has 8, etc.

10!=10*9*8*....*1 = 3628800

 

b) For this question, the order matters.  We will use the nPr formula.  n=10 r=5 10P5 = 30240

 

c) 1/30240