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.

omgitsrne Feb 15, 2024

#1**+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

EnormousBighead Feb 15, 2024

#1**+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