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How many paths are there from a to b, if every step must be up or to the right?

 May 15, 2020
 #1
avatar+111360 
+2

We  have  all  the possible  arrangements  of  this set   

 

{right, right, right, right, right, up, up, up up }

 

We can either  choose  any 5 of the 9 places to put  the "rights"  or  any 4 of the 9 places to place the "ups"

 

So

 

C(9,5)  =   C(9,4)   =    126 paths

 

 

cool cool cool

 May 15, 2020
 #2
avatar+57 
+1

the answer is 126 because in the end you are going to have to move 9 steps in all. So, 9 choose 5 equals 126.cheeky

 May 15, 2020

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