Let \(A = \{a, b, c, d, e, f, g, h\}\).
- Find the number of sequences of length 4 using elements of \(A\).
The number of elements in \(A\) is 8, so we expect \(8^4 = 4096\) sequences.
- Repeat part (a) if no letter is repeated.
\(P(8,4) = 8 \cdot 7 \cdot 6 \cdot 5 = 1680\).
- Repeat part (a) if the first letter in the sequence is \(b\).
Only 3 positions remain so \(8^3 = 512\).
- Repeat part (a) if the first letter is \(b\) and the last is \(d\) and no letters are repeated.
There are only 6 remaining elements in \(A\) (since \(b\) and \(d\) are already used) for the 2 remaining positions so \(P(6,2) = 6 \cdot 5 = 30\)