How many paths are there from C to B, if every step must be up or to the right?
+20 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.
