- Total players selected: 30
- Allotment:
- Senior Team: 15 players (half of 30)
- Junior Team: 15 players (half of 30)
- Preferences:
- Prefer Senior Team: 60\% of $30=18$ players
- Prefer Junior Team: 40\% of 30 = 12 players

We need to find the least possible number of players who are not assigned to their preferred team.

Step 1: Understand the Constraints
1. Senior Team Allotment: 15 slots
- Prefer Senior Team: 18 players
- Prefer Junior Team: 12 players
2. Junior Team Allotment: 15 slots
- Prefer Junior Team: 12 players
- Prefer Senior Team: 18 players

Step 2: Minimize Unhappy Players
To minimize the number of players not getting their preferred team:
- Assign as many players as possible to their preferred team within the allotment limits.

Case 1: Maximize Senior Team Preferences
- Senior Team Allotment (15 slots):
- Assign all 12 players who prefer Junior Team to the Junior Team (since they don't prefer Senior Team).
- Remaining slots in Senior Team: 15-0 = 15 (since none of the Junior-preferring players are assigned here).
- Assign 15 out of the 18 Senior-preferring players to the Senior Team.
- Unhappy Senior-preferring players: 18-15 = 3 (must be assigned to Junior Team).
- Junior Team Allotment (15 slots):
- Already has 12 Junior-preferring players.
- Add the 3 unhappy Senior-preferring players.
- Total: 12 (happy) +3 (unhappy) $=15$.

Case 2: Verify for Optimality
- If we assign fewer than 15 Senior-preferring players to the Senior Team, the number of unhappy players increases.
- For example, assigning only 14 Senior-preferring players to the Senior Team would leave 4 unhappy players (18-14 = 4).

Thus, the minimum number of unhappy players is 3 .
Step 3: Cross-Check
- Happy Players:
- Senior Team: 15 (all prefer Senior Team, but only 15 of the 18 can be accommodated).
- Junior Team: 12 (all prefer Junior Team).
- Unhappy Players:
- 3 Senior-preferring players must be assigned to the Junior Team.

Final Answer

The least possible number of unhappy players is A