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.