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04 Nov 2007, 11:37
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can someone please explain to me what is the difference between these two questions, why the same method doesnt work for both questions.
1) How many different outcomes are there when you toss a coin three times.
Answer: YOu have two different choices for each coin toss and you toss is three times, so its 2^3 =8 different outcomes.
2) Every morning, Casey walks from her house to the bus stop, as shown to the right. She always travels exactly nine blocks from her house to the bus, but she varies the route she takes every day. ( One sample route is shown). How many days can Casey walk from her house to the bus stop without repeating the same route?
(Diagram is attached, she starts at the bottom left and finishes at the top right)
Answer: 9! / (5! * 4!) = 126 ways
Why can't I solve 2 by saying Casey has two choices for each step of her route, she can either go up or to the right. and she makes a total of 9 steps. so 2^ 9 = 512 different ways.
1) How many different outcomes are there when you toss a coin three times.
Answer: YOu have two different choices for each coin toss and you toss is three times, so its 2^3 =8 different outcomes.
2) Every morning, Casey walks from her house to the bus stop, as shown to the right. She always travels exactly nine blocks from her house to the bus, but she varies the route she takes every day. ( One sample route is shown). How many days can Casey walk from her house to the bus stop without repeating the same route?
(Diagram is attached, she starts at the bottom left and finishes at the top right)
Answer: 9! / (5! * 4!) = 126 ways
Why can't I solve 2 by saying Casey has two choices for each step of her route, she can either go up or to the right. and she makes a total of 9 steps. so 2^ 9 = 512 different ways.
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04 Nov 2007, 12:16
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Jim u r not completely wrong in your reasoning....but consider this case (Fig attached) that u reach a corner, now u will have only one option. This will reduce the total no of routes.
I may be wrong...Some one please confirm
I may be wrong...Some one please confirm
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caseys_route_201.doc [26 KiB]
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