1. Joined
    19 Oct '03
    Moves
    69376
    13 Mar '05 23:26
    You and a friend are playing Scrabble, which involves lettered tiles. Here is the distribution of the tiles:

    A:9 B:2 C:2 D:4 E:12 F:2 G:3
    H:2 I:9 J:1 K:1 L:4 M:2 N:6
    O:8 P:2 Q:1 R:6 S:4 T:6 U:4
    V:2 W:2 X:1 Y:2 Z:1 Blank:2

    At the start of the game, you choose seven letters. Solve the following, showing all work.

    a) what is the probability that you will choose three vowels and four consonants? (counting 'Y' as a vowel)

    b) what is the probability that you will choose the letters A,B,C,D,E,F, and G in order?

    A calculator is going to be needed. Have Fun!
  2. Joined
    29 Feb '04
    Moves
    22
    14 Mar '05 05:034 edits
    Originally posted by TDR1

    a) what is the probability that you will choose three vowels and four consonants? (counting 'Y' as a vowel)

    b) what is the probability that you will choose the letters A,B,C,D,E,F, and G in order.


    There are
    9 A's
    12 E's
    9 I's
    8 O's
    4 U's
    2 Y's
    So total vowels = 44

    There are
    100 tiles
    2 Blanks
    So total consonants = 98 - 44 = 54

    a) Number of ways of arranging 3 vowels and 4 consonants = 7! / 3! 4! = 35
    Number of ways of choosing 3 vowels and 4 consonants in a particular order = (44*43*42)*(54*53*52*51) / (100*98*97*96*95*94*93)
    149586723 / 18796757000

    Hence probability of choosing 3 vowels and 4 consonants in any order
    149586723 / 537050200
    = 0.2785339676

    b) Required probability = 9*2*2*4*12*2*3 / (100*98*97*96*95*94*93)
    = 1 / 723675144500
    = 0.00000000000381835493

  3. Joined
    29 Feb '04
    Moves
    22
    14 Mar '05 09:282 edits
    Originally posted by THUDandBLUNDER
    Number of ways of choosing 3 vowels and 4 consonants in a particular order = (44*43*42)*(54*53*52*51) / (100*98*97*96*95*94*93)


    Oops, that should be
    Number of ways of choosing 3 vowels and 4 consonants in a particular order = (44*43*42)*(54*53*52*51) / (100*99*98*97*96*95*94)
    = 4532931 / 606347000

    Hence probability of choosing 3 vowels and 4 consonants in any order
    = 4532931 / 17324200
    = 0.2616531211

  4. Cincinnati, USA
    Joined
    28 Aug '04
    Moves
    9069
    15 Mar '05 02:25
    But that doesn't account for the possibility of one or two of the seven tiles being blanks, which can be used as either vowels or consonants.
  5. Joined
    29 Feb '04
    Moves
    22
    15 Mar '05 03:19
    Originally posted by Gyr
    But that doesn't account for the possibility of one or two of the seven tiles being blanks, which can be used as either vowels or consonants.
    I believe the question was about how the tiles are chosen, not about how they are played.
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