SOLUTION: Serial numbers for a product are to be made using 4 letters followed by 2 digits. The letters are to be taken from the first 6 letters of the alphabet, with no repeats. The digits

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Question 1144410: Serial numbers for a product are to be made using 4 letters followed by 2 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?
Found 2 solutions by Alan3354, ikleyn:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Serial numbers for a product are to be made using 4 letters followed by 2 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?
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6*5*4*3*10*9

Answer by ikleyn(52803) About Me  (Show Source):
You can put this solution on YOUR website!
.

ANSWER.  (6*5*4*3) * (10*9).


Explanation.  


6 options for the letters in the 1-st position.

5 options for the 5 remaining letters in the 2-nd position.

4 options for the 4 remaining letters in the 3-rd position.

3 options for the 3 remaining letters in the 4-th position.



10 options for the digits in the 5-th position.

 9 options for the 9 remaining digits in the 6-th position.


It gives the answer.

You compute the number.

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To see many similar solved problems, look into the lessons
    - Combinatoric problems for entities other than permutations and combinations
    - Miscellaneous problems on permutations, combinations and other combinatoric entities
in this site.

After reading these lessons, you will be trained in solution such problems and will get more confidence.


Also,  you have this free of charge online textbook in ALGEBRA-II in this site
    - ALGEBRA-II - YOUR ONLINE TEXTBOOK.

The referred lessons are the part of this online textbook under the topic  "Combinatorics: Combinations and permutations".


Save the link to this textbook together with its description

Free of charge online textbook in ALGEBRA-II
https://www.algebra.com/algebra/homework/complex/ALGEBRA-II-YOUR-ONLINE-TEXTBOOK.lesson

into your archive and use when it is needed.