Question

There is a pizza which is cut into 4 quarters. There are 5 different toppings. In how many ways can these 5 toppings be places on these 4 quarters such that each quarter can have only 1 topping and no two adjacent quarters have the same toppings?

Answer 1

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Here's your answer...

The first quarter can have any of the 5 toppings, so the total number of ways for that slice is 5.
Now, the second quarter can have any topping except the topping of the first quarter, which leaves 4 ways.
For the third quarter, we are not allowed to use the topping on the second quarter, but we CAN use the topping on the first quarter, which again gives us 4 ways.
For the fourth quarter, there are 4 ways to top it, since two have been used up by the first and third quarter BUT now we can use the topping on the second quarter.
The total number of ways are 5×4×4×4 = 320.

Now that I have discovered that there are 320 different ways of topping only 4 slices, with only 5 toppings, I'm gonna go order a pizza. :-P

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