How to find permutation notation - ACT Math
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In permutation notation, what does 8P4 represent?
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
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
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How many different ways can five books be lined up on a shelf?
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.
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.
Compare your answer with the correct one above
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.)
How many different ways can cheese slices be stacked in piles containing
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
more easily.
This is 
. That is a lot of cheese arrangements!
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
more easily.
This is
Compare your answer with the correct one above