# Homework Help: 8 discrete math questions

1. May 2, 2005

### Townsend

I don't know why but these types of problems always seem to kick my butt. Any how here they are and my best guesses as to the correct answer.

1. Danny has 12 different lures in his tackle box that he takes on a five day fishing trip. On each day of the trip he fishes with the same lure all day then puts the lure back into his tackle box. How many ways can this happen?

12^5 = 248832 ways.

2. Danny has 10 different lures in his big tackle box. He takes 7 of these and puts them in his little tackle box and goes fishing with his friend Brian. Danny takes three of his lures and loans them to Brian, who did not bring any lures. Danny and Brian each choose a lure and begin fishing., How many ways can this happen?

$${10 \choose 7} {7 \choose 3} {4 \choose 1} {3 \choose 1} = 50400$$

3. Danny starts the day with 9 different lures in his tackle box. He fished with one lure until he loses it on a snag. He then puts on a new lure and fishes with it until he loses that lure. He does this until he has lost 5 lures. Then Danny gets sad because he lost so many lures and goes home. How many ways can this happen?

9*8*7*6*5=15,120 ways.

4. Danny takes 4 different lures with him in his little tackle box. He catches 8 different fish that day. Danny tries to remember which fish bit on which lure. How many ways could this have happened?

I think this is equivalent to finding the number of functions from an 8 element set to a 4 element set. So I think the answer is 4^8 = 65536.

5. Danny takes 5 different lures with him in his little tackle box. He catches 13 yellow perch that day. Danny tries to remember how many perch he caught on each lure. How many ways could this have happened?
$${17 \choose 13} = 2,380$$

6. Danny goes to a fishing show. At a lure booth a salesman has 4 identical Rapala lures, 5 identical Mister Twister lures, 8 identical Hula popper lures and 14 identical silver minnow lures. Danny buys 6 lures from the salesman. How many ways could this have happened?

I really have no clue about this one but to take a shot in the dark I would think this would be the same as picking 6 from the total.
$${31 \choose 6}$$

7. Danny has 12 different lures in his big tackle box. He picks out 4 lures and puts them in his little tackle box and tells Brian to pick out three lures to put in his little tackle box. At the end of the day they put all the lures back in Danny's big tackle box. The next day Danny picks out 5 lures to put in his little tackle box and Brian picks out 4 lures to put in his little tackle box. How many ways could this have happened?

Just another shot in the dark but I guess,
$${12 \choose 4} {8 \choose 3} {12 \choose 5} {7 \choose 4} = 768398400$$

8. Danny is going to order lures from a catalog. The catalog has 12 different lures in it. Danny orders a total of 5 lures, how many ways can this happen?
$${16 \choose 5} =4368$$

Sorry if there are too many questions for you to want to tackle (no pun intended) but even if you only look at a couple I would appreciate it.

Thanks

Jeremy