Question

which of the following is not a requirement of the permutations rule, $_np_r=\frac{n!}{(n - r)!}$, for items that are all different?
choose the correct answer below.
a. order is not taken into account (rearrangements of the same items are considered to be the same)
b. order is taken into account (rearrangements of the same items are considered to be different)
c. exactly r of the n items are selected (without replacement)
d. there are n different items available.

Explanation:

Step1: Recall permutation concept

Permutation is about arrangements where order matters.

Step2: Analyze option A

In permutations, order is crucial. Rearrangements of same items are different, so this option is incorrect as it says order is not taken into account.

Step3: Analyze option B

Order is indeed taken into account in permutations, so this is a correct requirement.

Step4: Analyze option C

In the permutation formula $_nP_r$, we select exactly $r$ of the $n$ items without replacement, so this is a correct requirement.

Step5: Analyze option D

The formula $_nP_r$ is for $n$ different available items, so this is a correct requirement.

Answer:

A. Order is not taken into account (rearrangements of the same items are considered to be the same)