Question Type 3: Grouping items together Exercises

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?

Eleven books are arranged on a shelf. Three mathematics books must be placed together. How many arrangements are possible?

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.

Six married couples sit around a round table. In how many ways can they be seated if each couple must sit together?

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.)

Twelve students line up. Three siblings must stand together and two twins must also stand together. How many different lineups are possible?

Find the number of possible arrangements.

Eight people are to stand in a row. In how many ways can this be done if three sisters must stand together?

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?

Nine people sit around a circular table. In how many ways can they sit if two particular people must sit next to each other?

In how many ways can 6 students be arranged in a line if two particular students must stand together?

Ten runners line up at the start. Four friends insist on standing consecutively. How many possible starting orders are there?