>  chances of  six heads in a row in twenty tosses
>      6!/14! =  8.258936e-9
>  my wife thinks. why so low? it is because you have to do it
> in sequence of six.
> 00111111000000000000 is okay
> 01010101010100000000 is not

But, 01111111111111111 is also OK.  So is
     11111111111111111 and
     11111101111110111 and
     01111110111111000 etc. etc...

I interpret the question to mean you just need to have 6 heads in a row.
You can have more but not less.

Jeff