Basic combinations. (Urgent please help)

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pepeketua

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Apr 8, 2021
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i did the following question in a practice exam (word for word):
Brayden is buying a triple scoop ice cream.
The flavours are: Vanilla, Strawberry, Chocolate, Mint or Gum drop.
He chooses three different flavours.
How many different combinations can he have?

My answer for this question was 60.
Working:
5*4*3=60
However, the mark scheme said that the answer was 10. I don’t understand how I am meant to get that answer. Somebody help me please! (My exam is in three hours)
 
Basic Combination.png

Your mistake was to consider that the order was relevant, notice that if we considered the order important in the the problem, we would remove the p! factor and it would give 5!/(5-3)! = 5!/2! = (5x4x3x2x1)/(2x1) = 5x4x3 = 60. What you did was a simple permutation, and this is not the case. Don't forget to identify the situation well, and good luck to your exam.
 
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You say that the answer is 60. Fine. Can you list the 60 combinations?

I'll start you off:
v s c, v s m, v s g, ...
 
vsc, vsm, vsg, vcm, vcg, vmg, scm, scg, smg, cmg
Thank you - this helps a lot.
Is there any quicker way to solve a problem like this?
 
When you do 5*4*3=60, you are counting vsc, vcs, scv, svc, cvs, csv as different combinations but they aren't - they are the same 3 flavours.
Note that there are 3*2*1=6 ways you can choose these 3 flavours.
So the 60 you got needs to be divided by 6, because each set of 6 like the one above, should only be counted once.
 
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