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# 𝗣𝗟𝗘𝗔𝗦𝗘 𝗛𝗘𝗟𝗣!!!!!

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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 $$(5,7)$$?

I tried 757, but it wasn't right.

This is what I tried:

$$\frac{(5+7)!}{5!*7!}$$= 792 paths to (5,7).

$$\frac{(4+3)!}{4!*3!}$$= 35 paths to subtract.

792-35=757. But I guess that wasn't right.

thank you!!! :D

Apr 20, 2020
edited by lokiisnotdead  Apr 20, 2020
edited by lokiisnotdead  Apr 20, 2020
edited by lokiisnotdead  Apr 20, 2020

#3
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Total possibilities with no restrictions

12 steps altogether. 5 are horizontal   12C5=792  just as you got

Total number that go to (4,3)

7 steps to get from start to (4,3) four are horizontal = 7C4 = 35 ways

Number of ways from (4,3) to (5,7)

5 steps, 1 horizontal = 5 ways

35*5=175 ways to get from start to finish if you go through (4,3)

Number of ways to get from start to finish if you do not go through (4,3) is    792-175 = 617

Apr 20, 2020

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

Apr 20, 2020
#2
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hmmm that wasn't right.... :(

Apr 20, 2020
#3
+2

Total possibilities with no restrictions

12 steps altogether. 5 are horizontal   12C5=792  just as you got

Total number that go to (4,3)

7 steps to get from start to (4,3) four are horizontal = 7C4 = 35 ways

Number of ways from (4,3) to (5,7)

5 steps, 1 horizontal = 5 ways

35*5=175 ways to get from start to finish if you go through (4,3)

Number of ways to get from start to finish if you do not go through (4,3) is    792-175 = 617

Melody Apr 20, 2020
#4
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wow! thank you so much melody! :)

#5
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So my answer is confirmed as correct?

Melody  Apr 21, 2020
#6
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Yes!! It was correct, and the solution was on point!

:)