Let $A = \{1, 5, 9, 11, 15, 23\}$

1. Find the number of sequences of length 3 using elements of A.

Since elements can repeat we have: $6^3 = 216$

2. Repeat part (a) if no element of A is to be used twice.

$P(6,3) = 6 \cdot 5 \cdot 4 = 120$

3. Repeat part (a) if the first element of the sequence is 5.

Since $5$ is fixed in the first position the two remaining positions can be filled with any of the six elements: $6^2 = 36$

4. Repeat part (a) if the first element of the sequence is 5 and no element of A is used twice.

$P(5,2) = 5 \cdot 4 = 20$