Assume that there are 14 board members: 9 females, and 5 males including mark. there are 3 tasks to be assigned. note that assigning the same people different tasks constitutes a different assignment.

1) find the probability that both males and females are given a task.

2) find the probability that mark and at least one female are given tasks.

Total members = 14

Total tasks = 3

So, total outcomes =

1) Find the probability that both males and females are given a task.

No. of females = 9

No. of males = 5

Favorable events = 2 female 1 male + 2 male 1 male =

So,  the probability that both males and females are given a task:

=

=

=

So,  the probability that both males and females are given a task is 0.7417

2)Find the probability that Mark and at least one female are given tasks.

Since mark is fixed , so places are left

So, favorable events =  2 female + 1 female 1 male =

So,  the probability that Mark and at least one female are given tasks. :

=  

=  

=  

So, The probability that Mark and at least one female are given tasks is 0.9230

do you have a picture of the table