Bethany, Chun, Dominic, and Emily go to the movies. They choose a row with four consecutive empty seats. If Dominic and Emily must sit beside each other, in how many different ways can the four friends sit?
(A) 6
(B) 5
(C) 12
(D) 30
(E) 3
Solution 1

We can write out the possible arrangements, using the first initials of the four people, and remembering that there two different ways in which Dominic and Emily can sit side by side:

DEBC, DECB, EDBC, EDCB, BDEC, CDEB, BEDC, CEDB, BCDE, CBDE, BCED, CBED

There are 12 possible arrangements.

## Solution 2

Since Dominic and Emily must sit beside other, then we can combine then into one person either Domily or Eminic, depending on the order in which they sit - and their two seats into one seat.

We now must determine the number of ways of arranging Bethany, Chun and Domily into three seats, and the number of ways of arranging Bethany, Chun and Eminic into three seats.

With three people, there are three possible choices for who sits in the first seat, and for each of these choices there are two possible choices for the next seat, leaving the choice for the final seat fixed. So with three people, there are $3 \times 2=6$ possible ways that they can sit in three chairs.

So for each of the 2 ways in which Dominic and Emily can sit, there are 6 ways that the seating can be done, for a total of 12 seating arrangements.

ANswer: (C)