I know there are many coin toss problems out there. This however doesn't aim to find the probability, but the representation by the use of other pre-defined events. So here goes.
A coin is tossed N-times. Define a possible probability space for this experiment. We observe the events $A_{k}$ = "Tails at k-th toss" (k = 1,...,N), B = "Heads is never thrown" and C = "at least twice tails and at least once heads are thrown". Express the events B and C with the event $A_{k}$.
Have so far got $B = \bigcap_{k=1}^{N}A_{k}$ and $C = B^c \cap $ (exactly once tails U never tails). And for "never tails" i've got $(\bigcup_{k=1}^{N}A_{k})^c$. Any idea how to find "exactly once tails"?