Henry Ernest Dudeney/Puzzles and Curious Problems/288 - Seating the Party/Solution

by : $288$

 * Seating the Party

Solution
The number of ways of seating the party is $144$.

Proof
There are three choices of drivers and three choices of women to sit beside him.

Anyone else can sit with their back directly to the driver; there are four choices remaining.

The one beside them must be of a different gender; there are two choices remaining.

The last two people have two ways to fill in the remaining seats.

Therefore the number of ways to seat the party is:
 * $3 \times 3 \times 4 \times 2 \times 2 = 144$