(c) The total number of arrangements of 9 people is given by the factorial of 9, which is:

\(9! = 362,880\)

To find the number of arrangements where Mr Ahmed and Mr Baker are not standing next to each other, we first calculate the arrangements where they are together. Treat Mr Ahmed and Mr Baker as a single unit, so we have 8 units to arrange. The number of arrangements for these 8 units is:

\(8! = 40,320\)

Within their unit, Mr Ahmed and Mr Baker can be arranged in 2 ways (Ahmed-Baker or Baker-Ahmed), so we multiply by 2:

\(8! \times 2 = 80,640\)

The number of arrangements where Mr Ahmed and Mr Baker are not together is:

\(9! - 8! \times 2 = 362,880 - 80,640 = 282,240\)

(d) To find the number of arrangements where there is exactly one person between Mr Ahmed and Mr Baker, consider the three people (Ahmed, Baker, and the person between them) as a single unit. There are 7 other people to arrange, so we have 7 units to arrange:

\(7! = 5,040\)

Within the unit, the arrangement can be Ahmed-Person-Baker or Baker-Person-Ahmed, so there are 2 ways to arrange them:

\(2\)

There are 7 choices for the person between Mr Ahmed and Mr Baker:

\(7\)

The total number of arrangements is:

\(7! \times 2 \times 7 = 5,040 \times 2 \times 7 = 70,560\)