Answer:
Explanation:
To calculate the number of ways to select four children from a group of six boys and four girls, ensuring that at least one boy is selected, we need to consider two scenarios: selecting one boy and three children (Case 1), and selecting four boys (Case 2).
Case 1: Selecting one boy and three children
Here, we can choose one boy out of the six boys in 6 ways. The remaining three children can be selected from the remaining nine children (three boys and four girls) in (9 choose 3) ways.
Number of ways for Case 1 = 6 * (9 choose 3) = 6 * C(9, 3)
Case 2: Selecting four boys
In this case, we need to select four boys out of the six available boys in (6 choose 4) ways.
Number of ways for Case 2 = (6 choose 4) = C(6, 4)
Total number of ways to select four children with at least one boy = Number of ways for Case 1 + Number of ways for Case 2
Total number of ways = 6 * C(9, 3) + C(6, 4)
Evaluating the calculations:
C(9, 3) = 84
C(6, 4) = 15
Total number of ways = 6 * 84 + 15 = 504 + 15 = 519
Therefore, there are 519 different ways to select four children from a group of six boys and four girls, ensuring that at least one boy is selected.