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
of course it's C(19,8)
I'll give you an example:
let's say the prefix is of length 3
so the only combination is: 111 (it's the only one)
let's look at the prefix of length 4: the way I see it ,there is no way to build this kind of prefix,becuase there can't be a combination in which the number of 1's is larger than the number of 0's by 3
for the prefix of length 5 the combinations are:
11110,10111...etc
we need to check each prefix, until we get to the prefix of length 19
is it clear now?