Part 1.

1. Students are classified according to gender (male or female), status (regular or irregular), and field of specialization (mathematics, physics, business, or languages). Draw a tree diagram to find all possible classifications. Determine the total number of possible classifications of students.

2. In how many ways can 11 people be seated: (a) in a row? (b) in a round table?

Part 2.

1. There were 5 boys and 5 girls who went to watch a play. How many ways can they be seated in a row in the theatre hall if the boys and the girls must alternate?

2. Suppose 7 female and 6 male applicants have been successfully screened for 5 positions. In how many ways can the following compositions be selected?

a.) 5 people regardless of gender

b.) 3 females and 2 males

c.) at least 3 females

d.) 4 females and 1 male

e.) 5 females