Question 1135813: How many seven letter code words can be formed using a standard 26 letter
alphabet if the first letter has to be a C and the rest of letters are
different? And if the first two letters have to be a vowel and the rest of the
letters are different?
Found 2 solutions by VFBundy, Edwin McCravy:
Answer by VFBundy(438)   (Show Source):
You can put this solution on YOUR website! How many seven letter code words can be formed using a standard 26 letter alphabet if the first letter has to be a C and the rest of letters are different?
It's not exactly clear if the rest of the letters have to be different from just the 'C' or also different from one another (including the 'C'). I'll assume it's the latter, that all seven letters need to be different:
1 * 25 * 24 * 23 * 22 * 21 * 20 = 127,512,000
And if the first two letters have to be a vowel and the rest of the letters are different?
Again, I'm assuming that "the rest of the letters are different" means all the letters need to be different from one another, and not only different from the first two letters. However, when it says "the first two letters have to be a vowel" it does NOT say that the first two letters are not allowed to be identical vowels. Taking all this into consideration:
[(4/5) * 5 * 4 * 24 * 23 * 22 * 21 * 20] + [(1/5) * 5 * 1 * 25 * 24 * 23 * 22 * 21] = 87,983,280
What is happening here is that, 4/5 of the time, the first two vowels will be different. 1/5 of the time, the first two vowels will be the same.
Answer by Edwin McCravy(20056)  (Show Source):
You can put this solution on YOUR website! How many seven letter code words can be formed using a standard 26 letter
alphabet if the first letter has to be a C and the rest of letters are
different?
C _ _ _ _ _ _
Answer: 25 remaining letters POSITION 6 remaining spaces = 25P6 = 127512000
And if the first two letters have to be a vowel
That's 5 vowels POSITION 2 = 5P2
and the rest of the letters are different?
That's 24 remaining letters POSITION 5 = 24P5
Answer: (5P2)(24P5) = (20)(5100480)n = 102009600
Edwin
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