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# Marvin the fly

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Marvin the fly starts at (0,0). Each step, Marvin moves one unit right or one unit up. He is trying to get to the point (5,7). However, at (4,3) there is a frog that will eat him if he goes through that point. In how many ways can Marvin reach (5,7)?

could someone help me get the answer? I am confused. All help appreciated.  Thanks so much!

Jun 18, 2021

#1
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The number of ways is c(12,5) - c(7,2)*c(5,2) = 582.

Jun 18, 2021
#2
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Sorry, that's incorrect.

Guest Jun 18, 2021
#3
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This is blatantly a homework question so I'll just give a few hints...

First find the no. of routes to (5,7) and (4,3) and then subtract the latter from the former got it?

So, to get to (5,7) Marvin must take 5 steps right and 7 up in any order.

Similarly to get to (4,3) he does 4 right and 3 up in any order.

Now, no. of routes to (5,7)$$={12!\over 5!7!}$$

Similarly you can find the no. of routes to (4,3).

There you go, I've given enough hints for this one..😏

Jun 19, 2021