1. A coin is tossed 10 times, and the sequence of heads and tails is observed. How many of the possible outcomes contain three heads, with no two heads adjacent to each other?
2. Four mathematics books and seven history books are arranged on a bookshelf. In how many of the possible arrangements are no two mathematics books next to each other?
3. In how many ways can six people be seated in a row of ten chairs so that at least two adjacent chairs are vacant?
4. In 2015, there were three women and six men on the United States Supreme Court. In how many ways could the justices be seated in a row for a group picture where no women sat next to each other?