1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Combinations and ice cream

  1. Aug 30, 2013 #1
    1. The problem statement, all variables and given/known data
    To put it simply, there are 4 different flavors of ice cream, and 6 different toppings.

    a)how many sundaes are possible using one flavor of ice cream and 3 diff toppings?
    b)How many sundaes are possible using one flavour of ice cream and from 0 to 6 toppings?
    c)How many different combinations of flavors of 3 scoops of ice cream are possible if it is permissible to make all 3 scoops the same flavor?


    2. Relevant equations
    nCr


    3. The attempt at a solution
    a)4*(4C3) = 80
    b)4*(4C0)+4*(4C1) etc up until 6.. I get a 256.
    c) This is the part I'm not so sure at...

    For each scoop, there are 256 combinations.. so therefore we look at it from the perspective of the different combinations of whether the scoops are of the same flavor or not? like

    SSS, SDD, DDD, SSD, same and different

    so 256x3! ?
     
  2. jcsd
  3. Aug 30, 2013 #2

    LCKurtz

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    I agree with your first two. For the third, can't you just use the counting principle? How many choices for the first scoop, then for the second, then for the third?
     
  4. Aug 30, 2013 #3
    Oh, so its 4x4x4? since the same flavors are allowed.
     
  5. Aug 30, 2013 #4

    LCKurtz

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    Yes, that's all there is to it.
     
  6. Aug 31, 2013 #5
    For (a) and (b) look again at the number of toppings. You should have spotted this when you tried to calculate 4C6.
     
  7. Aug 31, 2013 #6
    hmm not sure why i wrote 4 instead of 6 lol.. but yeah i wrote 6 on my work.. sry for the confusion
     
  8. Aug 31, 2013 #7
    But using the counting principle for c) will distinguish between the same combinations; AAB will be different than ABA etc. The counting principle is used when the order matters, i.e. permutations.

    Say your flavours A, B, C and D. You can represent the combination AAA by ***|||, the combination AAB by **|*||, ABC by *|*|*|, BDD by |*||** etc... Can you use this to count the number of combinations of 3 flavours with repetition allowed?
     
  9. Aug 31, 2013 #8

    LCKurtz

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    Yes, I think you are correct. I must have been thinking ice cream cones instead of sundaes in my response. :redface: Altogether too much sugar I guess.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Combinations and ice cream
  1. Ice Cream Cone Problem (Replies: 11)

Loading...