SOLUTION: 12 stalks of flower consisting of 3 red flowers, 4 blue flowers and 5 white flowers will be attached onto a string to make a wreath of flowers. Calculate the number of ways to arra

Algebra ->  Permutations -> SOLUTION: 12 stalks of flower consisting of 3 red flowers, 4 blue flowers and 5 white flowers will be attached onto a string to make a wreath of flowers. Calculate the number of ways to arra      Log On


   

Question 1177524: 12 stalks of flower consisting of 3 red flowers, 4 blue flowers and 5 white flowers will be attached onto a string to make a wreath of flowers. Calculate the number of ways to arrange the flowers to make the wreath
Found 2 solutions by greenestamps, ikleyn:
Answer by greenestamps(13198) About Me  (Show Source):
You can put this solution on YOUR website!


Let R, B, and W represent red, blue, and white flowers. Then the problem is asking for the number of different arrangements of the 12 objects

RRRBBBBWWWWW

By a well-known counting principle, that number of ways is

12%21%2F%28%283%21%29%284%21%29%285%21%29%29

Use a calculator....

Answer by ikleyn(52778) About Me  (Show Source):
You can put this solution on YOUR website!
.

    12%21%2F%283%21%2A4%21%2A5%21%29 =  = 27720 different arrangements  in a linear string,


and  1%2F12  of this number, i.e.  %281%2F12%29%2A27720 = 2310 for the circular wreath.

Solved.

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See the lessons
    - Arranging elements of sets containing indistinguishable elements
    - Persons sitting around a cicular table
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 lessons are 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.