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A moped licence plate has two letters and then four numbers in it. How many plates can be made without duplicating, there are no plates with number zero?

Answer
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Hint: We should find all the possible ways of combination where there is no duplication and there are no zeros. So first we should find out all possible combinations with 2 letters and 4 digits. Then we will subtract that value with the total number of ways where there are2 letters and zeros.

Complete step-by-step answer:
We know that in the licence plate the first two are letters let us consider them as L1 and L2 and the next four are digits let us assume them to be N1,N2,N3andN4 (these digits are non-zero)
Hence the licence format is L1L2N1N2N3N4
Number of ways to select letter is 26 because there are 26 alphabets in English
Number of ways to select numbers is 9 (including 0)
Hence the total number of ways of selection including zero are
 =26×26×10×10×10×10
=6760000
Now, the number of ways of selecting zero is
 =26×26×1×1×1×1
=676
Hence, the total number of ways in which plates can be made without duplicating and no plates with number zero are
 =676000676=675324
So, the correct answer is “675324”.

Note: In this particular question the order doesn’t matter hence we didn’t use permutation. We only used combinations to solve this problem. A combination is basically the selection of an object irrespective of the order.