Posted by **Vicky** on Thursday, September 11, 2008 at 4:01pm.

I'm having trouble on how to figure something out. The question says a pizza place uses 5 toppings (a,b,c,d,e). How many different combinations can be made with the pizzas having 3 different topping? A

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**David Q**, Thursday, September 11, 2008 at 4:05pm
It's a question about factorials: the answer is the number of ways you can choose 3 from 5. You could enumerate them without too much difficulty, but the shortcut is to work out 5! / (3! x (5-3)!), where N! means N x (N-1) x (N-2) .... x 2 x 1.

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**Reiny**, Thursday, September 11, 2008 at 4:07pm
think of it this way:

The pizzamaker would have 5 ways to choose the first topping, then 4 ways to do the second topping and finally 3 ways for the third topping

so isn't that 5x4x3 or 60 ways

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**David Q**, Thursday, September 11, 2008 at 4:09pm
No - you're distinguishing between the 1st, 2nd and 3rd, which you don't need to do. ABC is the same as BCA, which is the same as CAB etc. You've got to allow for all the combinations that are the same.

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**David Q**, Thursday, September 11, 2008 at 4:10pm
In fact, every triple can occur in six different ways - so the answer is actually the 60 you identified, divided by 6.

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**Kristin;**, Thursday, September 11, 2008 at 7:41pm
do 5x3..

its fifteen(:

these ppl are so confusingg;

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**David Q.**, Sunday, September 14, 2008 at 1:39pm
Just for the record the answer is ten. They are: ABC, ABD, ABE, ACD, ACE, ADE, BCD, BCE, BDE and CDE.

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