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# Pathway problem

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Find the number of paths from P to Q, where each step is to the right or up.

Jun 22, 2021

#1
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Ito get to the middle point from p it takes 2 to the right and 3 up, so there Is 6 ways to get to the middle point.so applying this logic From the middle point to q we can apply the same logic you need to travel4 to the right and 3 up so 12, now we can mutiply 6 x 12, =72

Jun 22, 2021
#2
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Find the number of paths from P to Q, where each step is to the right or up.

1. Number of permutations of rruuu   $$\dfrac{(2+3)!}{2!3!}=\dfrac{5!}{2!3!} = \mathbf{10}$$

2. Number of permutations of rrrruuu  $$\dfrac{(4+3)!}{4!3!}=\dfrac{7!}{4!3!} = \mathbf{35}$$

So in total there are $$10*35=350$$ paths

Jun 23, 2021