T102 SECTION 9.5 Permut & Combin

ofpossibilitiesforthe nthorlastposition

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Unformatted text preview: bcad, bcda, bdac, bdca, cabd, cadb, cbad, cbda, cdab, cdba, dabc, dacb, dbac, dbca, dcab, dcba } When n(S) = 4 Using the Fundamental Counting Principle, we can develop a formula for counting the number of permutations of n objects: # of possibilities for the 1st position # of possibilities for the 2nd position # of possibilities for the 3rd position . . . # of possibilities for the nth or last position . . . So, if there are n objects, then the number of possible ways to arrange the objects in a row is the product of all the natural numbers from n to 1, inclusive. This expression is called n factorial and is denoted _________. FORMULA FOR PERMUTING n DISTINCT OBJECTS: If there are n objects, then there are n! ways to arrange them in a definite order with no repeats. n! = n (n – 1)(n – 2)(n – 3) . . . (3)(2)(1) EXAMPLES: 1. 2. 3. a. 6! b. 3! ∙ 4! c. 7! 3!5! d. 0! How many ways can you arrange 5 books on a shelf? How many ways could you arrange 9 crazy tweens in line waiting for Justin Bieber tickets? This formula only works when we are arranging ALL of the objects in a certain order. But wh...
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