6 Four families go to a theme park together. Mr and Mrs Lin take their 2 children. Mr O'Connor takes his 2 children. Mr and Mrs Ahmed take their 3 children. Mrs Burton takes her son. The 14 people all have to go through a turnstile one at a time to enter the theme park.
- In how many different orders can the 14 people go through the turnstile if each family stays together?
- In how many different orders can the 8 children and 6 adults go through the turnstile if no two adults go consecutively?
Once inside the theme park, the children go on the roller-coaster. Each roller-coaster car holds 3 people.
- In how many different ways can the 8 children be divided into two groups of 3 and one group of 2 to go on the roller-coaster?