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Unformatted text preview: buy pizza. How many ways could this be done? Notice that the order of the choosing does not matter. Sending Betty and Dave is the same as sending Dave and Betty, so you would not count both of these possible choices. Let’s look at this example more closely. Let’s list all possible permutations: (How many are there? 4P2 = ______________________ . Now list them.) Al & Betty Al & Carol Al & Dave Betty & Al Betty & Carol Betty & Dave Carol & Al Carol & Betty Carol & Dave Dave & Al Dave & Betty Dave & Carol Cross out the doubles. Count the remaining groups. ___________ This is the number of combinations. In general, when counting groups of size r chosen from n objects, we will need to divide the number of permutations by r! FORMULA FOR THE NUMBER OF COMBINATIONS OF n OBJECTS TAKING r AT A TIME: Cr = n nPr
n! = r!
r! (n r )! EXAMPLES: 1.
A teacher needs to choose 3 students to run an errand out of a class of 35 students. How many ways can this be done? 2.
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