Solved

How many different combinations can be made from 5 varieties of flowers?

Posted on 2010-09-16
7
1,149 Views
Last Modified: 2012-05-10
If I have 5 different varieties of flowers:
carnations, roses, mums, marigolds and lilies.
And I put 3 different varieties of flowers in a vase
For example, a vase might contain roses, carnations and lilies
How many different combinations can be made from the 5 varieties of flowers?

0
Comment
Question by:zimmer9
[X]
Welcome to Experts Exchange

Add your voice to the tech community where 5M+ people just like you are talking about what matters.

  • Help others & share knowledge
  • Earn cash & points
  • Learn & ask questions
  • 4
  • 2
7 Comments
 
LVL 11

Accepted Solution

by:
dougaug earned 500 total points
ID: 33697859
You can use combinatory analysis

Cx,y =   x!
          _________
          y! * (x - y)!

I

0
 
LVL 11

Expert Comment

by:dougaug
ID: 33697864
You can use combinatory analysis

Cx,y =   x!
          _________
          y! * (x - y)!


In you example:

C5,3 =        5!              =   120      =   120    = 120   = 10
            __________      _______     _____    ____
            3! * (5 - 3)!          6 * 2!        6 * 2       12
0
 
LVL 32

Expert Comment

by:phoffric
ID: 33697866
You want to pick 3 kinds of flowers out of 5. So that is:
5 things taken 3 at a time = 5 C 3 = 5!/[(5-3)!(3!)] = 5*4/2! = 20/2 = 10 combinations.
    http://www.mathwords.com/c/combination_formula.htm
    http://www.wolframalpha.com/input/?i=5+C+3
0
Independent Software Vendors: We Want Your Opinion

We value your feedback.

Take our survey and automatically be enter to win anyone of the following:
Yeti Cooler, Amazon eGift Card, and Movie eGift Card!

 

Author Comment

by:zimmer9
ID: 33697890
Does this equate to:

    5!                                     120
    --                                      ---        =  10
    3! * (5 - 3)!          =            6 * 2
0
 
LVL 32

Expert Comment

by:phoffric
ID: 33697912
Yes, same calculations as above.

Note that 5! = 5*4*3!
so that the 3! in the denominator cancels out with the 3! in the numerator, and then you have

5!
------------  = 5*4/2! = 20/2 = 10
3! * (5 - 3)!  
0
 
LVL 32

Expert Comment

by:phoffric
ID: 33697923
So, in general, taking R things out of N leads to this number of combinations:


     N!             N(N-1)...(N-R+1)(N-R)!
----------- = ------------------------------- = N(N-1)...(N-R+1)/R!
R!( N-R )!                          R!( N-R )!

Here the (N-R)! factor in the numerator cancels with the same factor in the denominator.
0
 
LVL 32

Expert Comment

by:phoffric
ID: 33697937
Here is the general form that I used with the concrete numbers:


     N!             N(N-1)...(R+1)(R)!
----------- = -------------------------- = N(N-1)...(R+1)/( N-R )!
R!( N-R )!                     R!( N-R )!

Here the R! factor in the numerator cancels with the same factor in the denominator.
0

Featured Post

Independent Software Vendors: We Want Your Opinion

We value your feedback.

Take our survey and automatically be enter to win anyone of the following:
Yeti Cooler, Amazon eGift Card, and Movie eGift Card!

Question has a verified solution.

If you are experiencing a similar issue, please ask a related question

Suggested Solutions

Title # Comments Views Activity
Relative Frequency Assessment 2 38
Percentage 6 63
Triangle - computing angles 3 61
ANOVA 3 43
This article provides a brief introduction to tissue engineering, the process by which organs can be grown artificially. It covers the problems with organ transplants, the tissue engineering process, and the current successes and problems of the tec…
When we purchase storage, we typically are advertised storage of 500GB, 1TB, 2TB and so on. However, when you actually install it into your computer, your 500GB HDD will actually show up as 465GB. Why? It has to do with the way people and computers…
Although Jacob Bernoulli (1654-1705) has been credited as the creator of "Binomial Distribution Table", Gottfried Leibniz (1646-1716) did his dissertation on the subject in 1666; Leibniz you may recall is the co-inventor of "Calculus" and beat Isaac…
Finds all prime numbers in a range requested and places them in a public primes() array. I've demostrated a template size of 30 (2 * 3 * 5) but larger templates can be built such 210  (2 * 3 * 5 * 7) or 2310  (2 * 3 * 5 * 7 * 11). The larger templa…

756 members asked questions and received personalized solutions in the past 7 days.

Join the community of 500,000 technology professionals and ask your questions.

Join & Ask a Question