by **LazyNK** Tue Feb 28, 2012 1:51 pm

Hey Noah,

I believe you must get used to the glue method for such problems. The slot method is possible, but very complicated. I am not sure how you arrived at the slot method results you mention, but the correct slot method is as follows ( and I'm sure looking at this solution, you'd see the advantage of the glue method) :

GMPJBC

Case 1 : M takes first slot from left, N takes third from left

Total possibilities = 1x4x1x3x2x1 = 24

Case 2 : M takes first slot from left, N takes fourth from left

Total possibilities=1x4x3x1x2x1=24

Case 3 : M takes first slot from left, N takes fifth from left

Total possibilities=1x4x3x2x1x1=24

Case 4 : M takes first slot from left, N takes sixth slot

Total possibilities=1x4x3x2x1x1=24

Total allowed possibilities where M takes first slot= 24x4 = 24 x # of allowed possibilities for N=96

Similarly we'd have Case5-Case7 where M takes the second slot from left (only three allowed possibilities for N for this case)=24x3=72

Similarly, Case8-Case10 where M takes the third slot from left (again only three allowed possiblities for N)=24x3=72

As again, Case11-Case13, M takes fourth slot from left(three allowed possiblities for N)=24x3=72

Case14-Case16, M takes fifth slot from left (three allowed possiblities for N)=24x3=72

Case17-Case20, M takes sixth slot from left ( Four allowed possiblities for N)=24x4=96

Thus total allowed possibilities=96x2+72*4=192+288=480

Hope it clarifies.

NK