Six people go to the movies. John and Jack are two of these six people. When the people get there, they find that these are only 4 seats available (next to each other). Realizing that not everyone will be able to go in to the movie theater, they buy all 4 tickets. If both John and Jack have to sit together, how many seating arrangements are possible?

Question

georgesyip · Answer

there should be 6 arrangement...i guess correct me if i am wrong

kropot72 · Answer

Initially, consider John and Jack as one person, and the number of seats to be three. The number of seating arrangements in this case will be 5C3. However John and Jack can swap places in each of these arrangements. Therefore the total number of arrangements is given by:
$$\large 2\times5C3=\frac{2\times5\times4\times3\times2}{2\times3\times2}=you\ can\ calculate$$

joannablackwelder · Answer

Makes sense, @kropot72 Thanks!

kropot72 · Answer

You're welcome :)