Algebra 2/Trig
12.1, 12.2 Practice Worksheet
Name: _________________________
Date: __________________________
Section I: Decide whether each scenario should be counted using permutations or
combinations. Explain your reasoning.
1. The number of ways 10 people can line up in a row for concert tickets.
2. The number of different arrangements of three types of flowers from an array of 20
types.
3. The number of three-digit pin numbers for a debit card.
Section II: Determine the number of outcomes for each scenario. SHOW ALL WORK and
circle your final answer.
1. Twenty singers are trying out for the spring musical. In how many different ways can the
director choose a duet, assuming that both roles are the same?
2. Twenty singers are trying out for the spring musical. In how many ways can the director
choose a lead and an understudy?
3. A box contains 20 marbles. How many ways can 5 marbles be chosen?
4. A high school needs four new teachers: two math teachers, a chemistry teacher, and a
Spanish teacher. In how many ways can these positions be filled if there are six
applicants for mathematics, two for chemistry and ten applicants for Spanish?
5. You have 12 books. Your bookshelf will hold nine books. How many ways could you select
nine books for the shelf?
6. You still have 12 books. Your smaller bookshelf will hold 5 books. How many ways could
you select and arrange 5 novels on the smaller bookshelf?
Section II: Determine the number of outcomes for each scenario. SHOW ALL WORK and circle
your final answer.
7. Eight toppings are available for a pizza. In how many ways can Rose choose three toppings?
8. Out of a group of 30 people, 20 of which are women, how many different committees of 6
people (3 men and 3 women) can be chosen?
9. How many ways can the letters of MATHEMATICS be arranged?
10. Lauren has 6 new shirts, 4 new pair of pants, and 2 new belts. How many outfits can she
create provided she must choose exactly one of each?
11. Eight people are boarding an aircraft. Two have tickets for first class and board before
those in the economy class. In how many ways can the eight people board the aircraft?
12. How many three-digit numbers can be formed if the number is at least 400?
13. Four couples have reserved seats in a row for a concert. In how many different ways can they
be seated if
a) there are no restrictions?
b) the two members of each couple wish to sit together?
14. In how many orders can four girls and four boys walk through a doorway single file if
a) there are no restrictions?
b) the girls walk through before the boys?
15. How many ways can the letters in the word BANANA be arranged?