Question

In their next game, they scored 30 points in the first quarter, including at least 18 free throws. In how many ways could they have scored 30 points with at least 18 free throws?

a) 1
b) 2
c) 3
d) 4

Answer 1

There are 6 ways they could have scored 30 points with at least 18 free throws.

Step-by-step explanation:

In order to determine the number of ways they could have scored 30 points with at least 18 free throws, we need to consider the different possibilities. Let's analyze:

1. If they scored exactly 18 free throws, they need to score an additional 12 points. This can be done in 1 way by getting 6 field goals.
2. If they scored exactly 19 free throws, they need to score an additional 11 points. This can be done in 2 ways: either by getting 5 field goals and 1 three-pointer or by getting 4 field goals and 2 three-pointers.
3. If they scored exactly 20 free throws, they need to score an additional 10 points. This can be done in 3 ways: either by getting 4 field goals and 2 two-pointers, by getting 3 field goals and 2 two-pointers and 1 three-pointer, or by getting 2 field goals and 4 three-pointers.

Therefore, the total number of ways they could have scored 30 points with at least 18 free throws is 1 + 2 + 3 = 6 ways.