Chapter 1 summaryCombinatorial Analysis•Fundamental counting principles:1.(multiplication principle)Say task 1 can be done inn1ways, task 2 can be done inn2ways,..., taskkcan be done innkways. Then if we wish to do all the tasks in sequence, i.e. task 1,followed by task 2, ... , followed by taskk(choosing just one of the available ways to do each ofthe tasks),then this can be done in n1·n2·. . .·nkways.2.(addition principle)Say we have just one task to do. If we havemways to do it and alsonways to do it (in which there is no overlap between the two sets of ways of doing it),then theone task can be done in m+n ways.•Permutations and combinations:Say we havendifferent objects and we wish to selectkof thoseobjects.1.(permutations)If we then wish to arrange thosekobjects in a row (so each different orderingof the objects in a row counts as a different selection) then there areP(n, k) =n(n-1)(n-2). . .(n-k+ 1)ways to do it (note that there arekfactors in this product). We call each such selection followed
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