hello

I have a test in a few days.

Could you help me with these two counting problems:

1)

a) what is the number of series (length 19)in which there are 8 0's and 11

1's?

answer: easy C(11,8) the problem is with part b:

b) among the series above, what is the number of series in which in any prefix with length at least 3 the number of 1's is larger than the number of 0's by 3?

well I really dont know how to solve this thing..help would be appreciated.

2) what is the number of length 4 cycles in the complete bipartite graph K(6,6)?

thanks for your help guys