Question

Choose the option that best completes the statement below. In finding the number of permutations for a given number of items, _____.

A) the number of permutations is limited by the number of items which are alike.
B) it doesn’t matter if some of them are indistinguishable .
C) the number of permutations is determined by the number of items that don’t repeat.
D) the number of permutations isn’t dependent on the items that repeat.

Answer 1

The number of permutations is limited by the number of items which are alike.

Explanation:

Honestly, options A and C seem both valid: one states that you're limited by how many items repeat, and the other states that you depend on how many items don't repeat. They seem two faces of the same coin to me.

However, the idea is the following: imagine you want to compute the permutation of 3 object. In general, the answer would be 6: you have

ABC

ACB

BAC

BCA

CAB

CBA

But what if two items would repeat? For example, let's change our set from ABC to AAC. The permutations would be

AAC

ACA

AAC

ACA

CAA

CAA

As you can see, the number of distinct permutation has halved. This is quite intuitive, because every permutation that used to switch A and B now switches A and A itself, so you don't notice any difference.