N2025 P2 Q7

Fred has \(8\) cards with the following digits on them.

\[2 \quad 3 \quad 3 \quad 4 \quad 5 \quad 7 \quad 7 \quad 8\]

Fred places the \(8\) cards in a row.

1. Find the number of different arrangements that can be made.[2]
2. Find the number of different arrangements that can be made which start and end with an even digit and have no two even digits next to each other.[3]
3. Find the number of different arrangements that can be made in which the even digits are all together.[2]
4. Given that the even digits are all together, find the probability that the odd digits are also all together.[1]