Question 1195311
.
How many ways can 2 purple, 3 yellow, and 2 blue bulbs be arranged in a string 
of Christmas tree lights with 7 socks?
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<pre>
This problem is about arranging a line of objects, 
where distinguishable/undistinguishable objects/items are.


Use the formula for it

    the number of distinguishable arrangements = {{{(2+3+2)!/(2!*3!*2!)}}}


where 2+3+2 = 7 is the total number of objects, and 2, 3 and 2 are the "multiplicities" 
of undistinguishable object.


The formula gives

    the number of distinguishable arrangements = {{{7!/(2!*3!*2!)}}} = {{{(1*2*3*4*5*6*7)/((1*2)*(1*2*3)*(1*2))}}} = {{{5040/(2*6*2)}}} = {{{5040/24}}} = 210.


<U>ANSWER</U>.  There are 210 distinguishable arrangements.
</pre>

Solved, answered and explained.


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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.