Math
posted by bikie on .
Hello,
I have a probability problem on combination that is not easy to solve for me, and I need help. Thank you.
Probleme:
Problem:
Little Caesar's Pizza had a commercial on tv that said you could buy 1 pizza and get another one free, with up to 5 toppings per pizza. The dialogue went something like this: The older person said, " 5 toppings per pizza , that is 10 different pizzas to choose from"
The little boy then said "no, it is 1,048,576 combinations" Do you think the little boy is right? show the operations to find the number of combinations.

There are two ways to look at this:
Put the two pizza's side by side, and offer the 5 toppings to each, one at a time. The customer has a choice of "yes" or "no" to each topping, ten times, so the number of ways the two pizza's can be made is at most 2^10=1024.
Since the two pizza's can be swapped, so we overcounted by 2, and the number of ways to order the two pizza's drop to 1024/2=512.
The other way is to calculate the number of ways we can order 1 pizza, which equals 2^5=32 by the same reasoning above. There are 32^2 ways to order two pizzas, except for the duplication. So the number of ways to order the two pizza would be 32^2/2=512, again. 
thank you for your help.I really appreciate it.

You're welcome!