Question

there are several sets of three different numbers whose sum is 14 that can be chosen from {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11]. how many of these sets contain a 3?

Answer 1

There are 4 different sets that contain the number 3 and have a sum of 14.

Step-by-step explanation:

To determine how many sets containing the number 3 have a sum of 14, we can consider 3 to be a fixed element of the set. This means we are looking for pairs of numbers from the given set {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11} that add up to 11 (since 14 - 3 = 11).

The pairs to consider would be (1,10), (2,9), (4,7), and 5,6. As each pair forms a set with 3, such as {3,1,10}, {3,2,9}, {3,4,7}, and {3,5,6}, there are 4 different sets that contain 3 and sum to 14.There are 4 different sets that contain the number 3 and have a sum of 14.