.
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.
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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.