PS - Combinatory

lilu wrote:Basically, the directions U-up and L-left --> UULLL can be arranged in 5!/2!*3! ways--> 10 ways because U is repeated twice and L is repeated three times.

yes.

well done.

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since ALL OF THE ANSWER CHOICES ARE SMALL NUMBERS, we can also attack this problem by just making a list of the possibilities. as with other solutions involving making lists, the only catch is that you have to ORGANIZE YOUR LIST according to some easily understood principle.

here's one such principle:
figure out the paths that go left, early. then move to the paths that go left at later times.

here are the paths that you'll find according to this principle:

l l l u u
l l u l u
l l u u l

l u l l u
l u l u l
l u u l l

u l l l u
u l l u l

u l u l l

u u l l l

... and then there were ten.

you could also trace out these paths visually, on the diagram, but of course i don't have the means to do that here.

it should be noted that this is the same list that you'd get by organizing a bunch of abstract U's and L's in alphabetical order.