All ACT Math Resources
Example Question #655 : Arithmetic
In permutation notation, what does 8P4 represent?
The expression 8P4 represents the number of permutations of 8 objects arranged 4 at a time. Thus, 8 x 7 x 6 x 5 = 1680
Example Question #656 : Arithmetic
How many different ways can five books be lined up on a shelf?
Order matters, so we use permutations: (5)(4)(3)(2)(1) = 120
There are five possibilities for the first book, four possibilities for the second book, three for the third, and two for the fourth, and one possibility for the last book.
Example Question #657 : Arithmetic
How many different ways can cheese slices be stacked in piles containing unique types if you are presented with a selection of different cheeses? (Presume that the order of the cheese slices does matter.)
Since the order matters, you are dealing with a permutation in this question. A permutation like this could be done with the equation:
For our values, this would be:
However, it is easiest just to think of this like it has slots. Into the first, you have choices, into the second , and so forth. This generates for you
This is . That is a lot of cheese arrangements!