gmobley10 wrote:An auto license plate is constructed using the following sequence of letters and digits. a letter, a letter, a digit, a letter, a digit and a letter. If letters I and O are not used, and other letters and digits can be repeated, how many license plates can be constructed?
Did you guys get the answer as 968,330,880?
Just to be sure:
- Lhe license plate is a follows:
letter, letter, digit, letter, digit, letter
- Repetition is allowed
- We cannot use the letters I and O
Let's take the task of creating a license plate and break it into stages.
Stage 1: Select first character (letter)
We have 24 letters to choose from, so we can accomplish stage 1 in
24 ways.
Stage 2: Select second character (letter)
We have 24 letters to choose from (since repetition is allowed), so we can accomplish stage 2 in
24 ways.
Stage 3: Select third character (digit)
We have 10 digits to choose from, so we can accomplish stage 3 in
10 ways.
Stage 4: Select fourth character (letter)
We have 24 letters to choose from, so we can accomplish stage 4 in
24 ways.
Stage 5: Select fifth character (digit)
We have 10 digits to choose from, so we can accomplish stage 5 in
10 ways.
Stage 6: Select sixth character (letter)
We have 24 letters to choose from, so we can accomplish stage 6 in
24 ways.
By the Fundamental Counting Principle (FCP) we can complete all 6 stages (and thus create a licence plate) in
(24)(24)(10)(24)(10)(24) ways
The GMAT would never require us to evaluate this.
Cheers,
Brent
Aside: For more information about the FCP, we have a free video on the subject:
https://www.gmatprepnow.com/module/gmat-counting?id=775
