### All ACT Math Resources

## Example Questions

### Example Question #655 : Arithmetic

In permutation notation, what does 8P4 represent?

**Possible Answers:**

1680

336

6720

210

**Correct answer:**

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

### Example Question #656 : Arithmetic

How many different ways can five books be lined up on a shelf?

**Possible Answers:**

150

100

60

120

80

**Correct answer:**

120

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.)

**Possible Answers:**

**Correct answer:**

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!

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