I'm having a hard time solving these problems. How do you solve them?
1) A family consisting of an old man, 6 adults and 4 children, is to be seated in a row for dinner. The children which to occupy two seats at each end and the old man refuses to have a child on either side of him. In how many ways can the seating arrangement be made for the dinner?
2) Ten guests are to be seated in a row. Three of them are to be seated togather. Of the remaining seven, two do not wish to sit next to each other. Find the number of possible arrangements.
3) The letters of the word ZENITH are written in all possible orders. If all the words are written in a dictionary, what is the rank of the word ZENITH?