# Let X represent the difference between the number of heads and the number of tails obtained when a coin is tossed 6 times. What are possible values of X?

$\begin{array}{1 1}1,2,4 \\ 0,3,6 \\ 0,2,4,6 \\ 1,3,5 \end{array}$

If a coin is tossed 6 times, the number of heads (or tails) can assume one of the following values: {0, 1, 2, 3, 4, 5, 6}.
In fact the number of heads + number of tails must be = 6.
If the number of heads = {0,1,2,3,4,5,6}, then the corresponding # of tails = {6-0, 6-1, 6-2, 6-3, 6-4, 6-5, 6-6} = {6,5,4,3,2,1,0}.
The (modulus) difference between the values in the two set of events X = {6-0, 5-1, 4-2, 3-3, 4-2, 5-1, 6-0} = {6,4,2,0,2,4,6}.
Therefore the possible values of X are 0, 2, 4 and 6.