1. How many 10-letter words with no repeated letters contain the five vowels in alphabetical order?
2. How many eight-letter words with no repeated letters contain all five vowels?
A "word" is interpreted to be a sequence of letters.
3. 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 in which the three women sat next to each other?
4. You, a friend, and four other people are to be seated in a row of six chairs. How many arrangements are there in which you and your friend are seated next to each other?