Bunuel wrote:
In State X, all vehicle license plates have 2 letters from the 26 letters of the alphabet followed by 3 one digit numbers. How many different license plates can State X have if repetition of letters and numbers is allowed?
A. 23,400
B. 60,840
C. 67,600
D. 608,400
E. 676,000
Take the task of creating as license plate and break it into
stages.
Stage 1: Select the first character
This must be a letter from the alphabet.
So, we can complete stage 1 in
26 ways
Stage 2: Select the second character
This must be a letter from the alphabet.
Also, since repetitions are allowed, we can complete stage 2 in
26 ways
Stage 3: Select the third character
This must be a digit (0, 1, 2, 3, 4, 5, 6, 7, 8, or 9)
We can complete stage 3 in
10 ways
Stage 4: Select the fourth character
This must be a digit.
Since repetitions are allowed, we can complete stage 4 in
10 ways
Stage 5: Select the fifth character
This must be a digit.
Since repetitions are allowed, we can complete stage 5 in
10 ways
By the Fundamental Counting Principle (FCP), we can complete all 5 stages (and thus create a license plate) in
(26)(26)(10)(10)(10) ways
Note, before we perform any calculations, we should recognize that (26)(26)
(10)(10)(10) = (26)(26)
(1000) So, the answer must end in
000Answer:
Note: the FCP can be used to solve the MAJORITY of counting questions on the GMAT. So, be sure to learn it.
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