QR Help: Combinations Problem

[Hannamsm]

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Hey guys, please help me understand the nCr rule for combinations. I keep seeing these problems and can't quite do it right.

Here's an example:

A florist purchased 3 yellow roses, 2 pink roses, and 5 red roses. How many 3 rose arrangements are possible?

Answer: 120

 

[Hannamsm]

so I figured it out... but in case any one was wondering:

N is the total number and R is the number you can take:

N=10
R=3

N!/R!(N!-R!)
10!/3!(7!)
(10*9*8) / (3*2*1) = 120 😀

 

[MansonTiles]

Hey guys, please help me understand the nCr rule for combinations. I keep seeing these problems and can't quite do it right.

Here's an example:

A florist purchased 3 yellow roses, 2 pink roses, and 5 red roses. How many 3 rose arrangements are possible?

Answer: 120

Combonation formula = n!/m! (n!-m!)


10 total roses = n = 10!

m = 3 roses arragnement = 3!

SO.....

10!/3! (10!-3!) =

10!/3! (7!) =

reduce the top.......10*9*8*7!/3*2 (7!)

7! cancels out.....answer 120 🙂

 

[Hannamsm]

Thanks!

 

[checkamundo]

how do you know when to use the combinations formula and when to use the permutations formula?

 

[MansonTiles]

permutation is used ONLY when the order of the arrangement MATTERS!

unlike the question above, which just asks an arrangment of 3 roses, in no particular order.