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

Guest Jan 2, 2022

#1**+1 **

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.

OrcSlop Jan 2, 2022