The staircase depicted below has 10 steps. As \"rewalk up the staircase we must always end on step 10. A slaircasewf'l losteps 1. How many paths can I take up the staircase? Each path is distinguished by which steps I touch. For example, one path is Start > S1 > S5 > S5 > S9 > S10. I'm allowed to step over as many steps as I wish with each step - as long as I end on step 10. Each step goes UP the staircase, never down. 2. How man},r ways can I take up the staircase if I step on exactly 4 steps (including step 10]. With each step, I must advance at least one step forward - I can not take a step and remain on the same step. 3. OPTIONAL (5 points extra credit]: How many paths up the stairs are there if with each step I'm allowed to skip at most one level. For example: Start ) SI } S3 3' S4 3- S5 3' 37 > 39 > 310 is one such path