The finale score In a soccer game is 4-3. How many different scores were possible at half time?
Team 1 across
team 2down
* 0 1 2 3 4
0 x x x x x
1 x x x x x
2 x x x x x
3 x x x x x
4 * 5 = 20
Thanks so much :)
To determine the number of different scores possible at half time in a soccer game with a final score of 4-3, we need to consider all the potential combinations of scores that could have led to this final outcome.
Here's one way to approach this problem:
1. Let's assume that Team A scored 4 goals and Team B scored 3 goals in the entire game.
2. At half time, we want to consider all the potential combinations of scores that could have occurred.
Let's list out the possibilities for Team A's score at half time and Team B's score at half time:
- Team A: 0 goals, Team B: 0 goals
- Team A: 0 goals, Team B: 1 goal
- Team A: 0 goals, Team B: 2 goals
- Team A: 0 goals, Team B: 3 goals
- Team A: 1 goal, Team B: 0 goals
- Team A: 1 goal, Team B: 1 goal
- Team A: 1 goal, Team B: 2 goals
- Team A: 1 goal, Team B: 3 goals
- Team A: 2 goals, Team B: 0 goals
- Team A: 2 goals, Team B: 1 goal
- Team A: 2 goals, Team B: 2 goals
- Team A: 2 goals, Team B: 3 goals
- Team A: 3 goals, Team B: 0 goals
- Team A: 3 goals, Team B: 1 goal
- Team A: 3 goals, Team B: 2 goals
- Team A: 3 goals, Team B: 3 goals
- Team A: 4 goals, Team B: 0 goals
- Team A: 4 goals, Team B: 1 goal
- Team A: 4 goals, Team B: 2 goals
- Team A: 4 goals, Team B: 3 goals
3. Counting the number of combinations, we have a total of 16 different scores possible at half time.
Therefore, there are 16 different scores possible at half time in a soccer game with a final score of 4-3.
To determine the number of different scores that were possible at half time, we need to consider the possible combinations of goals scored by both teams.
Assuming each team can score a maximum of 4 goals in a game, we can create a set of possible scores for one team and multiply it by the set of possible scores for the other team. This will give us the total number of different score combinations.
For simplicity, let's consider the maximum goals a team can score at half-time to be half of the maximum goals in a game (2 goals). Now, we need to determine the possible scores for one team, assuming they can score 0, 1, or 2 goals. The possible scores are:
0 goals: 0-0
1 goal: 1-0, 0-1
2 goals: 2-0, 1-1, 0-2
So, for one team, there are 5 possible scores at half-time. Since the same set of scores applies to the other team, we multiply this number by 5 to get the total number of different score combinations:
5 (possible scores for one team) * 5 (possible scores for the other team) = 25
Therefore, there were 25 different scores possible at half-time in the given soccer game.