Question 1153320: Serial numbers for a product are to be made using 4 letters followed by 4 digits. The letters are to be taken from the first 8 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?
Answer by ikleyn(52777)   (Show Source):
You can put this solution on YOUR website! .
Any one of the first 8 letters in the 1-st position gives 8 options.
Any one of the REMAINING 7 of the first 8 letters in the 2-nd position gives 7 options.
Any one of the REMAINING 6 of the first 8 letters in the 3-rd position gives 6 options.
Any one of the REMAINING 5 of the first 8 letters in the 4-th position gives 8 options.
Thus with 4 letters in the first 4 positions, you have 8*7*6*5 = 1680 options.
Same analysis works for digits in the following 4 positions, giving 10*9*8*7 = 5040 options.
These options are independent, giving 1680*5040 all possible serial numbers.
ANSWER. In all, 1680*5040 = 8467200 different serial numbers are possible.
Solved.
Consider my solution as a MANTRA to solve other similar problems.
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From my solution, you should learn and understand
1) how I used the fact that there are 4 positions for letters and 4 positions for digits ?
- Each of these facts gave me 4 factors to a product.
2) how I used the fact that there was no repeating for letters and digits ?
- Each of these facts provided DECREASING factors in the products.
3) how I used the fact that the letters were taken from the first 8 letters
and how I used the fact that the digits were from 0 to 9?
- It provided me the first factor of 8 for the letters and the first factor of 10 for the digits.
If you do understand it, then you understand the logic of the solution IN FULL.
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