4. Find the answer to each counting problem below. (a) Suppose you own 13 distinct bow ties. You are going on a 5-day trip and need to select a different tie for each day you will be gone (so you will...

4. Find the answer to each counting problem below.
(a) Suppose you own 13 distinct bow ties. You are going on a 5-day trip and need to
select a different tie for each day you will be gone (so you will select which tie to wear the first
day, which to wear the second, and so on). How many ways can you do this?

(b)  You are running late so decide to choose which tie to wear on which day later,
and just want to pick 5 ties to toss into your suitcase. How many ways can you do this?
(c) Explain the relationship between the two counting problems above both
numerically and in terms of bow ties. Be specific: don’t just say which is larger, say how many times larger it is, and why this makes sense.