Permutationsin simple terms are considering all possible ways of doing somethingwith also keeping in mind the order of the items involved. This iscan be represented by n!(n fraction). Inthis, the elements are rearranging in a one-to-one correspondencewith itself (Lial, Greenwell & Ritchey, 2012). Hence, coming upwith an order list, which is systematic in all the possible ways inwhich something can be done or presented.
Forexample, we have ten contestants, and we want to know how many can beawarded the top three positions. Then it would be
Howeverthis does not give, us the options the top three positions but ratherthe all the options of the whole series. In addition as seen in theexample, the Permutations considers the order. As when we go fromten, nine is not skipped but considered, as it is imperative tomaintain the order. Hence, for all of the options of the top threepositions to be identified, three is subtracted from ten to give us
10!/ (10-3)! =10*9*8= 720
Thus,the out of the ten people the options of the top three positions is720. The Permutations is very useful in this as it is evident thatits ability to observe order is very crucial in getting the top threepoisons. As no one can be the first and the second at the same time.
Inconclusion, the difference between Permutations and combinations isodder. In combinations, the order does not matter. For example it canbe Mary, John and James or John, Marry and James. As long as all theelements are present the its all right (Lial, Greenwell &Ritchey, 2012). However, with Permutations the order is important. Itis like the combination of a safe. If the combination is 620, then0-2-6 or 6-0-2 will not work.
Lial,M. L., Greenwell, R. N., & Ritchey, N. P. (2012). Finitemathematics (10th ed.). Boston, MA: Pearson Education.