Identify the following as Permutations, or Combinations (no need to solve). A book club offers a choice of 8 books from a list of 40. In how many ways can a member make a collection?

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BlackTom AI · Accepted Answer

Here is the task restated and each option considered in turn.

The question asks: Identify whether the scenario is a Permutations problem or a Combinations problem (no calculation required). A book club offers a choice of 8 books from a list of 40. How many ways can a member make a collection?

Option a: Permutation. This would be appropriate if the order in which the 8 books are chosen mattered. For example, selecting books A, B, C in that specific order would be different from B, A, C. Since the problem does not mention any ordering of the chosen books (only which titles are included in the collection), treating the 8 books as an ordered sequence would be inappropriate in this context.

Option b: Combination. This is used when the order of selection does not matter, only the subset of items chosen. Here, a collection is defined by which 8 titles are included, not by the sequence in which they are listed or read. Therefore, the scenario aligns with a combinations approach, where the number of ways is given by the binomial coefficient C(40, 8).

In summary, option a describes a situation where order would affect the count, which is not the case here, while option b describes the unordered selection that matches the problem statement. The distinction hinges on whether the arrangement order matters or not, and this problem treats the set of 8 books as an unordered collection.

MDM4U - Mathematics of Data Management 12 (2025-26) - A

Identify the following as Permutations, or Combinations (no need to solve). A book club offers a choice of 8 books from a list of 40. In how many ways can a member make a collection?

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