The Infinite House of Pancakes (IHOP) offers 35
different kinds of pancakes. You would like to order a
stack of three pancakes. How many different choices
do you have, considering that you care about the order in which the pancakes are stacked? (In other
words, pecan/blueberry/pecan is a different choice
from pecan/pecan/blueberry.)
(a) P(35,3)
(b) 75
(c) 35^3
(d) 3^35
(e) C(35,3)
(f) none of the above

Question

The Infinite House of Pancakes (IHOP) offers 35
different kinds of pancakes. You would like to order a
stack of three pancakes. How many different choices
do you have, considering that you care about the order in which the pancakes are stacked? (In other
words, pecan/blueberry/pecan is a different choice
from pecan/pecan/blueberry.)
(a) P(35,3)
(b) 75
(c) 35^3
(d) 3^35
(e) C(35,3)
(f) none of the above

anonymous · Answer

a.
If the problem says order, you use permutations.

anonymous · Answer

My professor said that the answer is C. I originally got A as the answer too. I have no idea how he got his answer.

geerky42 · Answer

C is correct: You have 35 choices for first stack, 35 choices for second stack, and 35 choices for third, therefore total choices you have is $\boxed{35^3}$

anonymous · Answer

That makes sense! Thanks. How do I know when do that method or to use permutation?

anonymous · Answer

when to do*

geerky42 · Answer

Basically, if repetition is allowed, you just multiply by how many choices you have, etc.

Permutation or combinations is used when repetition is not allowed, depending on whether order matters or not.

geerky42 · Answer

If your problem says that you cannot select same pancake more than one times, then answer would be A.

anonymous · Answer

Ah, okay! I understand!

anonymous · Answer

Thanks again :)

geerky42 · Answer

No problem