Combination and Permutations

Combination and Permutations

Combinations and permutations are mathematical terms referring to the grouping of the elements of a set into subsets. On the one hand, no order is followed when grouping these elements by combination since combinations operate on the principle that all constituent elements have the same significance. However, permutations follow a specific order, failure to which one will get a wrong outcome. Determining whether one will use a permutation or a combination depends on the conditions presented by the problem being solved (Abramson et al., 2017). For instance, if five people are required to join a team where they will perform similar roles, then using combinations will be satisfactory. That is because every member of the team is expected to perform a similar role; hence, there is no need to separate them. However, if the five people join a team where they perform different roles, then permutations will be necessary. As such, in a group where members will perform different roles, the first person may be the leader, whereas the second person may be charged with taking notes.

Further, there are more permutations than combinations in any given set. For instance, if there are three pieces of paper labeled A, B, and C on a table, they constitute a single combination regardless of how they are grouped- in rows or on top of one another. However, the case is different for permutations since they can bring multiple outcomes if one comes up with different subsets. The permutations of the labeled papers will be ABC, BCA, ACB, CBA, CAB, and BAC. In other words, permutations are ordered combinations, which makes it possible to come up with multiple elements from the same set.

References

Abramson, J. P., Openstax, & Rice University. (2017). College algebra. Samurai Media Limited.

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Respond to the following in a minimum of 175 words:

How can you determine if you need to use a combination or permutation to count the number of outcomes?
Which will usually have more outcomes? Why?
Provide an example in your explanation.