More applications of permutations and combinations including a discussion of poker hand combinations.

1. There are 9 chairs in a row. In how many ways can 4 students be seated in
consecutive chairs?

2. Consider the digits 1, 3, 5, 7, 9. If repetitions are allowed, find:
(a) how many 3 digit numbers can be formed.
(b) How many 3 digit numbers can be formed if they must be less than
600 and divisable by 5.

3. In how many ways can 8 books be arranged on a shelf if 3 particular books
must be together?

4. Given a standard deck of 52 cars, how many ways are there to draw 5 cards
to obtain each hand.
(a) Royal Flush
[ace, king, queen, jack, ten in the same suit]
(b) Straight flush
[five cards in sequence and of the same suit, but not ace king queen jack
ten]
(c) Four of a kind
[four cards of one face value and one other card]
(d) Full house
[3 cards of one face value and 2 cards of another face value]

5. (e) Flush
[5 cards of the same suit but not in sequence, not including the
straight flush and royal flush above]

6. (f) Straight
[5 cards in sequence, but not all of same suit. Ace high or low]

7. (g) Three of a Kind
[exactly 3 cards of one face value and 2 different cards]

8. (h) Two pairs
[one pair of each two different face values and a card of a third face
value]
.

9. There are 10 football teams in a certain conference. How many games must be
played if each team is to play every other team just once?

10. Seven people reach a fork in a road. In how many ways can they continue their
walk so that 4 go one way and 3 the other?

11. (i) One pair
[two of one face value, and 3 cards of different face values, no
matching the pair]
(j) No pairs
[5 different face values, not in sequence, not all cards in the same
suit]
HOMEWORK