Assume that there are 18 board members: 12 females, and 6 males including Larry. There are 4 tasks to be assigned. Note that assigning the same people different tasks constitutes a different assignment.
To find the number of different ways to assign the tasks among the board members, we can use combinations and permutations.
Since there are 4 tasks and 18 board members, we need to select 4 members for each task. In this case, the order is not important, as assigning the same people different tasks would create a different assignment.
To calculate the number of ways to select 4 members out of 12 females, we can use the combination formula:
C(n, r) = n! / (r!(n-r)!)
n = 12 (number of females)
r = 4 (number of members to select for each task)
C(12, 4) = 12! / (4!(12-4)!)
= 12! / (4!8!)
= (12 * 11 * 10 * 9) / (4 * 3 * 2 * 1)
= 495
So, there are 495 different ways to assign the tasks among the 12 females.
Next, we need to select 4 members out of 6, including Larry, who is already one of the members. Since Larry is included in every assignment, we have 3 remaining spots to fill.
Using the combination formula, this can be calculated as:
C(5, 3) = 5! / (3!(5-3)!)
= 5! / (3!2!)
= (5 * 4) / (2 * 1)
= 10
So, there are 10 different ways to assign the tasks among the 6 males, including Larry.
To find the total number of ways to assign the tasks, we multiply both results together:
495 * 10 = 4950
Therefore, there are 4950 different ways to assign the 4 tasks among the 18 board members.