Question 1192088
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How many 6-digit numbers can be formed from the digits of 747 457?
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<pre>
In clear form, this problem asks  


      " how many different distinguishable words of given digits can be formed ? "



There are 6 digits; of them, the digit "7" has multiplicity 3 and digit "4" has multiplicity 2.


THEREFORE, the number of distinguishable arrangements of the given digits is  {{{6!/(3!*2!)}}} = {{{720/(6*2)}}} = {{{720/12}}} = 60.


<U>ANSWER</U>.  60 different 6-digit numbers.
</pre>

Solved.


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To see many other similar &nbsp;(and different) &nbsp;solved problems, &nbsp;look into the lesson

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF =https://www.algebra.com/algebra/homework/Permutations/Arranging-elements-of-sets-containing-undistinguishable-elements.lesson>Arranging elements of sets containing indistinguishable elements</A> 

in this site.


Also, &nbsp;you have this free of charge online textbook in ALGEBRA-II in this site

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/complex/ALGEBRA-II-YOUR-ONLINE-TEXTBOOK.lesson>ALGEBRA-II - YOUR ONLINE TEXTBOOK</A>.


The referred lesson is the part of this online textbook under the topic &nbsp;"<U>Combinatorics: Combinations and permutations</U>". 



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.