It's a problem from GMAT institute.
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?
it's PS problem, but not an official, so it has no option
the answer is 2100
but I don't know how to get this answer..
please someone help me..
math letter counting PS
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- Castor.kim
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Take the task of creating the code and break it into stages.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?
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
- Castor.kim
- Junior | Next Rank: 30 Posts
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- Joined: Thu Aug 30, 2012 10:23 pm
Thanks a lot Brent, after seeing your solution.. it looks simple and easy
I had solve it using..
21C2 * 5C1 * 2!(first and third letters change)..
I know.. looks stupid..
Thanks again Brent!!
I had solve it using..
21C2 * 5C1 * 2!(first and third letters change)..
I know.. looks stupid..
Thanks again Brent!!