Final answer:
There are 19,880 different teams of 4 that can be chosen from a group of 15 adults and 16 children if each team must have at least one child on it.
Step-by-step explanation:
To calculate the number of different teams of 4 that can be chosen from a group of 15 adults and 16 children, while ensuring that each team has at least one child, we need to consider two cases:
Case 1: One child and three adults are chosen in a team.
The number of ways to choose one child out of 16 children is 16. And the number of ways to choose three adults out of 15 adults is Combination(15, 3) = 455. So the total number of teams in this case is 16 x 455 = 7,280 teams.
Case 2: Two children and two adults are chosen in a team. The number of ways to choose two children out of 16 children is Combination(16, 2) = 120.
And the number of ways to choose two adults out of 15 adults is Combination(15, 2) = 105. So the total number of teams in this case is 120 x 105 = 12,600 teams.
Therefore, the total number of different teams of 4 that can be chosen while adhering to the given conditions is 7,280 + 12,600 = 19,880 teams.