Solved

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

Posted on 2010-09-16
7
1,183 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
Technology Partners: 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

On Demand Webinar: Networking for the Cloud Era

Did you know SD-WANs can improve network connectivity? Check out this webinar to learn how an SD-WAN simplified, one-click tool can help you migrate and manage data in the cloud.

Question has a verified solution.

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

A Guide to the PMT, FV, IPMT and PPMT Functions In MS Excel we have the PMT, FV, IPMT and PPMT functions, which do a fantastic job for interest rate calculations.  But what if you don't have Excel ? This article is for programmers looking to re…
We are taking giant steps in technological advances in the field of wireless telephony. At just 10 years since the advent of smartphones, it is crucial to examine the benefits and disadvantages that have been report to us.
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…
I've attached the XLSM Excel spreadsheet I used in the video and also text files containing the macros used below. https://filedb.experts-exchange.com/incoming/2017/03_w12/1151775/Permutations.txt https://filedb.experts-exchange.com/incoming/201…

688 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