Question Type 3: Grouping items together Bootcamps

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

Five differently colored flags are to be displayed in a vertical line. In how many ways can this be done if the two red flags must be adjacent?

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

Nine players are to line up for a team photo. In how many ways can they line up if three boys must stand together?

Seven books are to be placed on a shelf. Volumes 2, 3 and 4 of a series must be together and in order. How many arrangements are possible?

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

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

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

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

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.)

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?