.
How many ways can 2 purple, 3 yellow, and 2 blue bulbs be arranged in a string
of Christmas tree lights with 7 socks?
~~~~~~~~~~~~~~~~~~~
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 =
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 = = = = = 210.
ANSWER. There are 210 distinguishable arrangements.
Solved, answered and explained.
-------------------
To see many other similar (and different) solved problems, look into 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.