Castor.kim wrote:
A code consists of three of the 26 letters. The first and third letters are different consonants and the second letter is a vowel. How many such codes are possible?
Take the task of creating the code and break it into stages.
Stage 1: Select the first letter
Since this letter must be a consonant, and since there are 21 consonants, this stage can be completed in (
21 ways).
Stage 2: Select the second letter
Since this letter must be a vowel, and since there are 5 vowels (a, e, i, o, u), this stage can be completed in (
5 ways).
Stage 3: Select the third letter
Since this letter must be a consonant, and since we already used 1 consonant for the first letter, there are now 20 consonants remaining.
So, this stage can be completed in (
20 ways).
By the Fundamental Counting Principle (FCP) we can complete all 3 stages (and thus create a 3-letter code) in
(21)(5)(20) ways ([spoiler]= 2100 ways[/spoiler])
Aside: For more information about the FCP, we have a free video on the subject:
https://www.gmatprepnow.com/module/gmat-counting?id=775
Cheers,
Brent
