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Combination or Permutation, please help

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Combination or Permutation, please help

by [email protected] » Fri Aug 01, 2008 12:56 am
Hi

I am really struggling to see when to answer a counting question using combintaiton or using permutation - Anyone got any tips to graps these concepts better?

I have a book with a whole bunch of combo and perm examples and for instance here is a very simple one:

Theresa ordered a combo pizza with 3 different toppings. If there are 6 toppings to choose from and one of her toppings is mushrooms, how many different combo pizzas did she have to choose from?

I thought this was a combination problems and as there mushrooms are fixed it was a 5C3 so the answer is 10? Well its not the answer is 20? C

Can someone please explain this to me!
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Re: Combination or Permutation, please help

by Ian Stewart » Fri Aug 01, 2008 3:46 am
[email protected] wrote: I have a book with a whole bunch of combo and perm examples and for instance here is a very simple one:

Theresa ordered a combo pizza with 3 different toppings. If there are 6 toppings to choose from and one of her toppings is mushrooms, how many different combo pizzas did she have to choose from?

I thought this was a combination problems and as there mushrooms are fixed it was a 5C3 so the answer is 10? Well its not the answer is 20? C
It's a pizza, so the order of the toppings doesn't matter (pineapple, mushrooms and bacon is the same pizza as bacon, mushrooms and pineapple). If we know we have mushrooms, we need to choose 2 toppings from the remaining 5, which we can do in 5C2 ways. Equivalently, we can choose 3 toppings to leave off of the pizza, which we can do in 5C3 ways. Either way, the answer should be 10, so either there's something else in the question (perhaps a choice of two different cheeses, which would double the answer?), or the book you're using has the wrong answer. Out of curiosity, what book is it? In any case, your interpretation is entirely correct.
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by sudhir3127 » Fri Aug 01, 2008 5:14 am
just my 2 cents on it...

i think 20 is correct .. as we have already chosen ...

choosing 1 topping out of 5 will in 5 ways,,
choosing another topping out 4( having exhausted 2 topping options) is 4 ways.

hence its 5*4 = 20. ( i think its a permutation question )
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by beeparoo » Fri Aug 01, 2008 1:40 pm
sudhir3127 wrote:just my 2 cents on it...

i think 20 is correct .. as we have already chosen ...

choosing 1 topping out of 5 will in 5 ways,,
choosing another topping out 4( having exhausted 2 topping options) is 4 ways.

hence its 5*4 = 20. ( i think its a permutation question )
Pff. There's NO WAY that this problem, as worded, is a permutation problem. How can the order of the toppings matter on a pizza??

Unless, the pizza has layers; like a bottom pepperoni layer, a middle mushroom layer, and top pineapple layer. Either way, it better be DELICIOUS!
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by Ian Stewart » Fri Aug 01, 2008 6:38 pm
beeparoo wrote:
Unless, the pizza has layers; like a bottom pepperoni layer, a middle mushroom layer, and top pineapple layer.
Brilliant- a layered pizza. A perfect illustration of when order should matter, and when it should not. Nice one!
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