Serial numbers for a product are to be made using 3 letters followed by 3 numbers. if the letters are to be taken from the first 6 letters of the alphabet with no repeats and the numbers are taken from the digits 0 through 9 with no repeats, how many serial numbers can be generated

11,232,000

This result is a single number slightly over 11 million




Work Shown:

Throughout all of this, order does matter (eg: ABC is different from BCA)

Focus on the letters for now
There are 26 letters total. 
The first slot has 26 choices
The second slot has 25 choices (since we can't reuse whatever is in slot1)
The third slot has 24 choices

For just the letters only, we have 26*25*24 = 15600 permutations

Since we'll use this number later, let's call this M = 15600


Now onto the numbers. There are 10 digits total
For slot 1 we have 10 choices
For slot 2 we have 9 choices
For slot 3 we have 8 choices

For just the numbers only, we have 10*9*8 = 720 permutations

Since we'll use this number later, let's call this N = 720


Now multiply M and N
M*N = 15600*720 = 11,232,000

So we can generate 11,232,000 serial numbers

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