there are 4 possible scoring plays in NFL football game:touchdown=6 points;point after touchdown=1 point;feildgoal=3 points;and safty=2 points

a. how many different ways could the team score 11 points?
b. what final scores, between 1 and 30, are not possible for a team to make?

4,19

To find the different ways a team can score 11 points in an NFL football game, we can break down the scoring options and calculate the combinations.

a. To score 11 points, we need to consider the four possible scoring plays: touchdown (6 points), point after touchdown (1 point), field goal (3 points), and safety (2 points).

Let's start by listing out the possible scoring combinations:

1) Touchdown + Field Goal + Point After Touchdown => 6 + 3 + 1 = 10 points
2) Touchdown + Safety + Field Goal => 6 + 2 + 3 = 11 points

Therefore, there are two different ways a team can score 11 points.

b. To determine the final scores between 1 and 30 that are not possible for a team to make, we need to consider all the possible scoring combinations and see which ones fall within that range.

We can start by listing the possible scores:

1) Touchdown (6 points)
2) Touchdown + Point After Touchdown (7 points)
3) Touchdown + Field Goal (9 points)
4) Touchdown + Point After Touchdown + Field Goal (10 points)
5) Touchdown + Safety (8 points)
6) Touchdown + Safety + Point After Touchdown (9 points)
7) Touchdown + Safety + Field Goal (11 points)
8) Touchdown + Safety + Point After Touchdown + Field Goal (12 points)
9) Field Goal (3 points)
10) Field Goal + Point After Touchdown (4 points)
11) Safety (2 points)

Now, let's analyze the final scores that are not possible between 1 and 30:

1, 2, 3, 4, 5, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29.

These are the final scores between 1 and 30 that are not possible for a team to make in an NFL football game.