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T102 SECTION 9.5 Permut & Combin

r1r2r3rk examples

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Unformatted text preview: here are “like” objects involved, we use a different formula. Let’s look at an example: List all arrangements of the letters in the word “ZOO”? Make a tree diagram: List all arrangements of the letters in the word “RED”? Make a tree diagram: {ZOO, OZO, OOZ} {RED, RDE, ERD, EDR, DRE, DER} “RED” = ____________ Now, how many different ways were you able to find? “ZOO” = ____________ Why are they different when they both have 3 letters? FORMULA FOR PERMUTING WITH LIKE OBJECTS (REPEATS) If a set of n objects, of which r1 are of one kind, r2 are of another kind, and so on through rk, then the number of possible permutations of all n objects is: _______n!______ r1! r2! r3! ... rk! EXAMPLES: Find the number of ways the letters in the following words can be arranged: a. BUBBLE b. STATISTICS III. COMBINATIONS Combinations are just groups where the order of the objects in the group does not matter. For instance, suppose we have a club with 4 members, Al, Betty, Carol, and Dave. They need to send 2 people from the club to...
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