Ten students are to stand in a line. A particular group of 3 must stand together and another group of 4 must also stand together. How many arrangements are possible?
[4](No specification provided)
Eleven books are arranged on a shelf. Three mathematics books must be placed together. How many arrangements are possible?
[3]A group of nine players consists of three boys and six girls. They are to line up for a team photo. Find the number of ways they can line up if the three boys must stand together.
[3]Six married couples sit around a round table. In how many ways can they be seated if each couple must sit together?
[4]A necklace is to be made from 8 distinct beads. In how many ways can the necklace be arranged if three specific beads must be adjacent? (Rotations and reflections of the necklace are considered identical.)
[4]Twelve students line up. Three siblings must stand together and two twins must also stand together. How many different lineups are possible?
[3]Seven books are to be placed on a shelf. Volumes 2, 3 and 4 of a series must be together and in order.
Find the number of possible arrangements.
[3]Eight people are to stand in a row. In how many ways can this be done if three sisters must stand together?
[2]Five differently coloured flags, including a red flag and a blue flag, are to be displayed in a vertical line. In how many ways can this be done if the red and blue flags must be adjacent?
[4]Nine people sit around a circular table. In how many ways can they sit if two particular people must sit next to each other?
[4]In how many ways can 6 students be arranged in a line if two particular students must stand together?
[4]Ten runners line up at the start. Four friends insist on standing consecutively. How many possible starting orders are there?
[4]