Thread: Permutation Problem involving letters

Problem:
We wish to construct three-letter words from the twenty six letters of the English alphabet.
How many possibilities are there, if the word must come before EGG in alphabetical order.
No letter may be used more than once in a word.

I have an answer. I would just like to confirm if my process of thinking is right.

Originally Posted by FennecFox

Problem:
We wish to construct three-letter words from the twenty six letters of the English alphabet.
How many possibilities are there, if the word must come before EGG in alphabetical order.
No letter may be used more than once in a word.
I have an answer. I would just like to confirm if my process of thinking is right.

If you post that answer along with your reasoning, we can comment.

Sure. I didn't post it because I didn't want someone to look at my reasoning and make a bias decision on the outcome of the answer

Case 1: If the first letter is A to D

1. Choose the first letter, A to D .... 4 ways
2. Choose a second letter .... 25 ways (A-D cannot be used)
3. Choose a third letter .... 24 ways (A-D + second letter cannot be used)

Case 2:If the the first letter is E

1. Choose the first letter to be E ... 1 way
2. Choose the second letter to be between A-F ... 5 ways (cannot pick E)
3. Choose a third letter ... 24 ways (cannot pick E or second letter)

Case 3:If the first letter is E and the second letter is G

1. Choose the first letter to be E ... 1 way
2. Choose the second letter to be G ... 1 way
3. Choose the third letter to be between A-F ... 5 ways (cannot pick E)

Adding together all 3 cases I get (4x25x24) + (5x24) + (5) = 2525

EDIT: Also I would be thankful if anyone could help me on my related post.

Originally Posted by FennecFox

Sure. I didn't post it because I didn't want someone to look at my reasoning and make a bias decision on the outcome of the answer

Case 1: If the first letter is A to D

1. Choose the first letter, A to D .... 4 ways
2. Choose a second letter .... 25 ways (A-D cannot be used)
3. Choose a third letter .... 24 ways (A-D + second letter cannot be used)

Case 2:If the the first letter is E

1. Choose the first letter to be E ... 1 way
2. Choose the second letter to be between A-F ... 5 ways (cannot pick E)
3. Choose a third letter ... 24 ways (cannot pick E or second letter)

Case 3:If the first letter is E and the second letter is G

1. Choose the first letter to be E ... 1 way
2. Choose the second letter to be G ... 1 way
3. Choose the third letter to be between A-F ... 5 ways (cannot pick E)

Adding together all 3 cases I get (4x25x24) + (5x24) + (5) = 2525

EDIT: Also I would be thankful if anyone could help me on my related post.

That looks good.