Given a standard deck of 52 cars, how many ways are there to draw 5 cards
 to obtain each hand.

(a) Royal Flush
[ace, kin...
(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]
(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]
Colours
In how many ways can 4 balls be drawn together from a bag containg 5 red balls, 7 white balls, and 3 green balls? ...
Pre-Cal 40S Slides December 3, 2007
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Pre-Cal 40S Slides December 3, 2007

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Combinations, permutations and poker hands.

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Pre-Cal 40S Slides December 3, 2007

  1. 1. 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]
  2. 2. (e) Flush [5 cards of the same suit but not in sequence, not including the straight flush and royal flush above]
  3. 3. (f) Straight [5 cards in sequence, but not all of same suit. Ace high or low]
  4. 4. (g) Three of a Kind [exactly 3 cards of one face value and 2 different cards]
  5. 5. (h) Two pairs [one pair of each two different face values and a card of a third face value]
  6. 6. (i) One pair [two of one face value, and 3 cards of different face values, no matching the pair]
  7. 7. (j) No pairs [5 different face values, not in sequence, not all cards in the same suit]
  8. 8. Colours In how many ways can 4 balls be drawn together from a bag containg 5 red balls, 7 white balls, and 3 green balls? How many of these ways include: (a) 2 red and 2 white balls? (b) just 2 white balls? (c) only white balls? (d) balls of only one colour? (e) no red balls? More Points Ten points are marked in a plane, no three of them lying in a straight line. How many triangles do they determine? Beads From 10 beads of different colours, how many bracelets of 6 beads each can be formed? Books From 7 French and 9 English books, in how many

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