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

 

 Jan 2, 2022
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In total, we must make 10 steps, 2 up, and 8 to the right.  

 

In order to do this, we must choose  any 2 out of the 10 moves to go up.  

 

Examples are R R U R R R R U R R

 

The number of ways to do this is 10 choose 2, \({10 \choose 2}\), or \(\fbox{45}\) as the final answer.  

 

You should note that because we can never travel down, anything below C (the entire 3rd row) is irrelevant in computing the answer.  

 Jan 2, 2022

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