(i) To find the number of possible arrangements of seating Mary, Ahmad, Wayne, Elsie, and John with no restrictions, we calculate the number of permutations of 5 people out of 40 seats:
\(^{40}P_5 = \frac{40!}{(40-5)!} = 78,960,960\)
(ii) For the second part, we need to consider two groups: Mary and Ahmad sitting together in the front row, and Wayne, Elsie, and John sitting together in one of the other rows.
First, consider the arrangement of Wayne, Elsie, and John in any of the 7 other rows. There are 3! ways to arrange them in a row:
\(3! = 6\)
Since there are 7 rows available, the total number of ways to arrange Wayne, Elsie, and John is:
\(7 \times 6 = 42\)
Next, consider Mary and Ahmad sitting together in the front row. They can be arranged in 2 ways:
\(2! = 2\)
There are 4 possible pairs of seats they can occupy in the front row:
\(4 \times 2 = 8\)
Therefore, the total number of arrangements is:
\(42 \times 8 = 336\)
However, the mark scheme indicates a total of 1,008, suggesting a different interpretation or calculation. Following the mark scheme:
For the 7 rows: \(7 \times 18 = 126\) ways
For the front row: \(4 \times 2 = 8\) ways
Total: \(126 \times 8 = 1,008\)