(1) (5+5+5 points) A bus starts at John M. Greene with 6 people, not including t
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Question
(1) (5+5+5 points) A bus starts at John M. Greene with 6 people, not including the bus driver. lets all those people off (and no others on-it's very early in the morning) by the time it reaches Amherst College. There are 8 stops at which passengers might get off. The driver needs to record certain passenger information to assess how popular each of the stops are. (a) Suppose the driver only needs to record the number of people leaving at each bus stop. How many possibilities are there? (b) Suppose the driver cares about the individual people leaving at each bus stop. How many ways are there for the driver to record the names of people leaving at each stop? (o) How many ways are there for the driver to record the names of people leaving at each stopit at most one person gets off at each stop?Explanation / Answer
Here we can say we have to select/choose people for stops.
Hence ,
a) Only the number is important we will use combination =C(8,6) = 28 ways
b)Names are important so 6 people have to chosse from 8 stops that is 8*8*8*8*8*8 =262,144 ways
c)Atmost 1 person at each stop
That means 2 stops will have no people getting off at
These 2 stops can be selected in C(8,2) = 28 ways
Every way will have 6! ways of assinig passengers to their respective busstops
=6!*28 = 20,160 ways
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