Describe a scenario that would require permutation and combination.

An election where candidates are elected and then allotted specific roles is a scenario that would require both combinations and permutations.

Expert Answers

An illustration of the letter 'A' in a speech bubbles

A combination refers to the number of ways of choosing a certain number of elements when the order in which they are chosen is not relevant. Permutations on the other hand refer to picking elements in a certain order. Given n elements from which r have to be chosen, the number of possible combinations is `C(n, r) = (n!)/(r!*(n-r)!)` while the number of permutations is `P(n,r) = (n!)/(n-r)!` .

A scenario that requires the use of both combinations and permutations is analyzing an election. If there are N candidates standing in the elections for a total of R seats, the number of ways in which the candidates can be selected by the voters is C(N,R). Here, the order is not relevant. For instance, the number of ways of choosing 3 candidates from a total of 10 is C(10, 3) = 120. Now, the elected candidates have to take on one of the roles of president, vice-president or CEO, the number of ways in which this is possible is given by a permutation, P(3, 3) = 6 . We cannot use a combination here as the order is relevant here.

Last Updated by eNotes Editorial on
Soaring plane image

We’ll help your grades soar

Start your 48-hour free trial and unlock all the summaries, Q&A, and analyses you need to get better grades now.

  • 30,000+ book summaries
  • 20% study tools discount
  • Ad-free content
  • PDF downloads
  • 300,000+ answers
  • 5-star customer support
Start your 48-Hour Free Trial