Since 2001, the standard serial numbers on a New York state license pl

Question

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 .

littlewarthog · Answer

Answer E.

Since the 7 positions are completely independent from each other, we simply need to multiply the possibilities for each of the 7 positions. Each of the three letters allows 26 combinations (assuming 26 different letters) and the digits allow 10 different combinations for each position. We therefore get:

26 * 26 * 26 * 10 * 10 * 10 * 10 = 26^3 * 10 ^4 = 26 ^3 * 10,000

beattheheat · Answer

Solution:
3 repeated letters can be chosen as 26 * 26 * 26
4 repeated digits can be chosen as 10 * 10 * 10 * 10
Answer E

Bunuel · Answer

OFFICIAL 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).

akshay605 · Answer

Would the answer be A if the letters and numbers were not allowed to be repeated

Bunuel · Answer

In this case B would be correct: (26 × 25 × 24) × (10 × 9 × 8 × 7)

altairahmad · Answer

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.

TheNightKing · Answer

altairahmad 
Hello, The question is asking how many combinations are possible in total. We are not concerned whether the number plates are same or not. So Lets say AAA0000 next will be AAA0001 next will be AAA0002 and so on.. So All we need to figure out is what is the number of exhaustive cases.

bumpbot · Answer

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Since 2001, the standard serial numbers on a New York state license pl

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