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How many ways can you write two different letters chosen from
A B C D E F G H I J K L M N O P
so that they are in alphabetical order, and the first letter is a vowel?  For example, AF and EN count, but DE and KC do not.

 Feb 15, 2024

Best Answer 

 #1
avatar
+1

There are 4 vowels and the rest 12 are consonants. 
There are 4 cases:

CASE 1: A
If one picks A as the first letter then there are 15 more choises to pick.

Case 1 has 11 choises

CASE 2: E
the second letter must be anything starting from F meaning 11

CASE 3: I
there are 7 choises

CASE 4: O
there is only one choice which is P

Therefore
\(15+11+7+1=\boxed{34}\)
(NOTE: this is not counting AA, EE, II, AND OO. if so just add 4 to 34= 38)
ggwp

 Feb 15, 2024
 #1
avatar
+1
Best Answer

There are 4 vowels and the rest 12 are consonants. 
There are 4 cases:

CASE 1: A
If one picks A as the first letter then there are 15 more choises to pick.

Case 1 has 11 choises

CASE 2: E
the second letter must be anything starting from F meaning 11

CASE 3: I
there are 7 choises

CASE 4: O
there is only one choice which is P

Therefore
\(15+11+7+1=\boxed{34}\)
(NOTE: this is not counting AA, EE, II, AND OO. if so just add 4 to 34= 38)
ggwp

EnormousBighead Feb 15, 2024

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