SOLUTION: A home improvement store has the following house numbers: 335666 left after a sale. How many different six-digit house numbers can be made from those numbers?

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Question 1160676: A home improvement store has the following house numbers: 335666 left after a sale. How many different six-digit house numbers can be made from those numbers?
Answer by ikleyn(52915)   (Show Source): You can put this solution on YOUR website!
.

As the condition says, the store has two digits { 3 ";  one digit  " 5 ", and 3 digits  " 6 ".


So, in all there are 6 digits at the store;

of them, digit  3  has the multiplicity of 2;

         digit  5  has the multiplicity of 1;

    and  digit  6  has the multiplicity of 3.


The number of all possible different six-digit arrangements of these digits is


     =  = 120.


In the formula, 6! is the number of all possible permutations of 6 different digits;

the factors in the denominator account for repeating arrangements, that occur due to presence of indistinguishable digits.

Solved.

-----------------

See the lesson
    - Arranging elements of sets containing indistinguishable elements
in this site.

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

The referred lesson is 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.


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