permutation and combination

Question

A coin is tossed 14 times .heads occur 18 times and tail 6 times . the second and thirteenth tosses are heads then find maximum no of heads that can occur in a row?

Answer 1

Assuming 14, 8 and 6.

 

                    1       
12345678901234
  H                     H

Since we must use the two given flips of heads, that leaves only six flips to position somewhere (anywhere) in the sequence.  We want a position that creates the maximum number in a row.
 
Placing six heads in positions 3-8 or in positions 7-12 create a string of 7 heads in a row.  We can’t do any better than that.

Answer 2

Did you mean the coin was tossed 24 times?  Or did you mean head occurred 8 times?  One of those needs to be changed.