Bunuel wrote:
Bunuel wrote:
Tough and Tricky questions: Combinations.
Since 2001, the standard serial numbers on a New York state license plate are 3 letters followed by 4 digits. How many different license plates are possible if letters and digits can be repeated?
A. 26 × 3 × 10 × 4
B. 26 × 25 × 24 × 10 × 9 × 8 × 7
C. 26³ × 9 × 9 × 9 × 9
D. 26 × 25 × 24 × 10 000
E. 26³ × 10 000
Kudos for a correct solution.(E) The formula for permutations of events is the product of the number of ways each event can occur. There are 26 letters and 10 digits. So there are 26 × 26 × 26 options for the three letters, and 10 × 10 × 10 × 10 for the four digits. The number of different license plates is 26 × 26 × 26 × 10 × 10 × 10 × 10 = 26³ × 10 000.
The correct answer is choice (E).
Hi,
I have a slight confusion about this problem.
Since all the answers are permutations, when we say 26 x 26 x 26 x 10 x 10 x 10 x 10 aren't we saying that order matters ?
What I mean to say is that there might very well be a number plate with
CLL 1234 and as two Ls will be taken as different under this permutation based method the total count will include another
CLL 1234, whereas hey should be counted as just 1 (2 number plates can not be the same).
Shouldn't we make an adjustment for this ?
Will appreciate a response on this please.
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76% (00:56) correct 
