(i) To find the number of different outfits, multiply the number of choices for each item: shoes, jeans, and tee shirts. Thus, the total number of outfits is:

\(4 \times 3 \times 7 = 84\)

(ii) First, calculate the total number of arrangements of 10 items (3 jeans + 7 tee shirts):

\(10! = 3628800\)

Next, calculate the arrangements where the two blue items are together. Treat the two blue items as a single unit, reducing the problem to arranging 9 items:

\(9! = 362880\)

Within this unit, the two blue items can be arranged in \(2!\) ways:

\(2! = 2\)

Thus, the number of arrangements where the blue items are together is:

\(9! \times 2 = 725760\)

Subtract this from the total arrangements to find the number of ways the blue items are not together:

\(10! - 9! \times 2 = 2903040\)

(iii) Fahad can choose any number of books from 1 to 9. The number of ways to choose at least one book is the total number of subsets of 9 books minus the empty set:

The total number of subsets is \(2^9\):

\(2^9 = 512\)

Subtract the empty set:

\(512 - 1 = 511\)