- 13 Mar '05 23:26You 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! - 14 Mar '05 05:03 / 4 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

- 14 Mar '05 09:28 / 2 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