Serial numbers for a product are to be made using 2 letters followed by 3 digits. The letters are to be taken from the first 6 letters of the alphabet, with no repeats. The digits are taken from the 10 digits 0, 1, 2, ..., 9, with no repeats. How many serial numbers can be generated?

Explanation:

There are 6 letters to pick from {A,B,C,D,E,F} and we have two slots to fill, where no repeats are allowed. This means we have 6*5 = 30 different ways to pick two letters.

There are 10 digits to pick from {0,1,2,...,9} and there are 3 slots to fill. This gives 10*9*8 = 720 different permutations for this portion.

Overall, we have 30*720 = 21600 different serial numbers possible.

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