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There are 9 chairs in a row. In how many ways can 4 students be seated in
consecutive chairs?
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.
In how many ways can 8 books be arranged on a shelf if 3 particular books
must be together?
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]
(e) Flush
   [5 cards of the same suit but not in sequence, not including the
straight flush and royal flush above]
(f) Straight
    [5 cards in sequence, but not all of same suit. Ace high or low]
(g) Three of a Kind
   [exactly 3 cards of one face value and 2 different cards]
(h) Two pairs
   [one pair of each two different face values and a card of a third face
value]




                                            .
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?
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?
(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

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Pre-Cal 40S Slides April 24, 2007

  • 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