Posted by John on Wednesday, March 3, 2010 at 5:32pm.
I will do the 2 vowels for you
since she grabbed 3 letters it could have been
VVC, VCV, or CVV
look at the first, the VVC
there are 3 vowels out of 9 prob (first a vowel) = 3/9
so now there are 8 letters left, 2 of them vowels
prob (second a vowel) = 2/8
so now the third letter must be a consonant, and there are 7 letters left, 6 of them consonants.
Prob(third is a consonant) = 6/7
Prob(first a vowel, 2nd a vowel, third a cons) = 3/9 x 2/8 x 6/7
now can you see how she would get the VCV of
3/9 x 6/8 x 2/7 setup ?
and for the CVV it would be 6/9 x 3/8 x 2/7
did you notice that the numerators are simply
2x3x6 and the denominators are 9x8x7 just in different order?
Does it matter what order you do multiplication?
so the prob would be
Now see if you reason out the others in the same way.
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