Question

A photographer is taking a picture of a bride and groom together with $6$ attendants. How many ways can he arrange the $8$ people in a row if the bride and groom stand in the middle?

Answer 1

Find the arrangement of 8 people in a row.

There are eight people containing six attendants and two are bridge and groom.

The position of bridge and groom is fixed at the middle. Thus if the bridge and groom are at the middle, there are three people are to be arranged at the left end three at the right end.

The six people can be arranged in $6!$ ways with bridge and groom at the middle of the row.

Since the position of bridge and groom can be arranged in two ways, the total number of ways the six attendants and the bridge and groom can be arranged is:

$$\begin{gathered} 2\times 6!=2\times 6\times 5\times 4\times 3\times 2\times 1 \\ =1440 \end{gathered}$$

Hence, the numbers of ways the eight people can be arranged in the row is $1440$.