SOLUTION: Can someone check my work on this problem? City Pizza makes a specialty pizza with 4 layers of toppings alternating with layers of cheese and advertises that they offer 26 diffe

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Question 635778: Can someone check my work on this problem?
City Pizza makes a specialty pizza with 4 layers of toppings alternating with layers of cheese and advertises that they offer 26 different toppings.
A) How many different pizzas can be made if none of the toppings can be duplicated and the order of the toppings matters?
26*25*24*23 = 358,800
B) How many different pizzas can be made if none of the toppings can be duplicated and the order of toppings doesn't matter?
26!/4!(26-4!)=14,950
Any help would be great, thank you so much
Found 2 solutions by solver91311, ewatrrr:
Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!


You can't do better than perfect. Good job.

The only thing I might have done differently would be to express the first one as:



and then show your arithmetic, just to demonstrate that I really know what is going on. The second one is:



if you want to get fancy on that one also.

John

My calculator said it, I believe it, that settles it
The Out Campaign: Scarlet Letter of Atheism

Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
 

Hi,

City Pizza makes a specialty pizza with 4 layers of toppings alternating with layers of cheese 

and advertises that they offer 26 different toppings.

 A) How many different pizzas can be made if none of the toppings can be duplicated and the order of the toppings matters?

Yes.  26P4 = 26*25*24*23 = 358,800 

B) How many different pizzas can be made if none of the toppings can be duplicated and the order of toppings doesn't matter?

Yes.  26C4 = 26!/4!(26-4!)=14,950 

Was wondering... as to alternating layers...that could double each amount..

if, in fact, that was to be taken into account

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