Permutations and Combinations
1. a) How many different 7-place license plates are possible if the first 3 places are for
letters and the other 4 for numbers?
b) Repeat part (a) under the assumption that no letter or number can be repeated in a
single license plate.
2. In an 8 person race, in how many ways can gold, silver and bronze be awarded?
3. There are 15 juniors in a drawing for the last 4 parking spaces. In how many ways can
the 4 spots be given?
4. To win the lottery, you must correctly select 6 numbers from a group of 48 (1 through
48). The order of the numbers is not important. How many different tickets could
5. A softball team has 15 players. How many ways can they fill the 9 distinct positions
on the field?
6. A church has 7 bells in its tower. Before a service, 5 bells are rung. If none of them
are rung more than once, how many possible sequences are there?
7. A CD club allows you to choose 6 CDs from a group of 20. How many possibilities?
8. There are 25 people in a 4th grade class who will compete for 3 awards (Math, Science
and English). In how many ways can these 3 awards be given?
9. In a group of 20 people, if everyone shakes hands with everyone else once, how many
handshakes will there be?
10. If a student has to sell 2 books from a collection of 6 Math, 4 Science, and 5 English,
how many ways are possible if a) the books can be any subject? b) the books have to be
from the same subject?
11. In a weightlifting competition of 10 people, 4 from the U.S., 3 from Russia, 2 from
Sweden and 1 from Norway, how many ways could they finish if the standings only show
the country that they represent?
12. From a group of 5 women and 8 men, how many different committees consisting of
2 women and 3 men can be formed if two of the men refuse to work together?
13. A committee consisting of 2 Republican, 2 Democrats, and 3 Independents is to be
chosen from a group of 5 Republican, 6 Democrats, and 4 Independents. How many
committees are possible?
14.Assume 3 men and 3 women go to a movie. How many ways can they sit together if…
a) they can sit anywhere?
b) all the boys have to sit together and all the girls have to sit together?
c) a boy can’t sit next to a boy, and a girl can’t sit next to a girl?
d) they are married couples and each couple has to sit together?