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

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

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.