SOLUTION: A combination is made by selecting three letters from the alphabet. How many combinations are possible if the letters can't be a vowel and don't repeat? With explanations, pl

Question 881911: A combination is made by selecting three letters from the alphabet.
How many combinations are possible if the letters can't be a vowel and don't repeat?
With explanations, please!
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
You have 26 letters. Five of them are vowels. So there are 26-5 = 21 consonants.

You have
21 choices for slot 1
20 choices for slot 2 (notice how 21-1 = 20)
19 choices for slot 3 (21-2 = 19)

Multiply the choices out: 21*20*19 = 7,980

So there are 7,980 different permutations. This is where order matters. So BCD is different from CBD.

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If order doesn't matter, then you divide by 3! = 3*2*1 = 6 to get 7,980/6 = 1,330

This means there are 1,330 combinations (order does not matter). With combinations, BCD is the same as CBD because those 3 letters are together which means they are the same group.
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