(a) (i) The number of ways to choose 6 books from 18 is given by the combination formula \(\binom{18}{6}\). Calculating this gives:

\(\binom{18}{6} = \frac{18 \times 17 \times 16 \times 15 \times 14 \times 13}{6 \times 5 \times 4 \times 3 \times 2 \times 1} = 18564\)

(ii) To include the Harry Potter book, choose 5 more books from the remaining 17. This is \(\binom{17}{5}\):

\(\binom{17}{5} = \frac{17 \times 16 \times 15 \times 14 \times 13}{5 \times 4 \times 3 \times 2 \times 1} = 6188\)

(b) (i) The total number of ways to arrange 8 people (5 boys and 3 girls) is \(8!\):

\(8! = 40320\)

(ii) Treat the 5 boys as a single unit. This gives 4 units to arrange (3 girls + 1 unit of boys). The number of ways to arrange these 4 units is \(4!\). Within the boys' unit, the 5 boys can be arranged in \(5!\) ways. Therefore, the total number of arrangements is:

\(5! \times 4! = 120 \times 24 = 2880\)