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Test2_with_solutions - 1(12 points 20 people have applied...

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1. (12 points) 20 people have applied for parking permits. There are 4 parking lots. a. How many ways are there to assign each person to a lot if all that matters is which lot they are assigned and lot A has 4 spots lot B has 6 spots lot C has 7 spots lot D has 3 spots 20! 3!4!6!7! = ( 20 4 )( 16 6 )( 10 7 )( 3 3 ) b. What if there is only one parking spot and each spot is numbered (i.e. now the spaces are distinguishable) 20! c. In how many of the parking assignments from part b) is person 1 assigned spot 1 and person 2 is assigned some parking spot numbered between 1 and 10? There are 1*9*18! ways to assign the spots. The first person has only one choice, the second has 9 possibilities, and everyone else can be assigned anywhere. There are 18 people remaining, so there are 18! to arrange them, since they are distinguishable and spots are distinguishable and only one person can have each slot. 1
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2. (16 points) Find the number of ways to distribute 20 Crime Scene Investigators to 5 crime scenes if it doesn’t matter which CSI we send to each scene (all that matters is the
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