Section 2.2-2.3
MATH 166:503
February 19, 2015
Topics from last class: multiplication principle, generalized multiplication principle, factorials, permutations, number of permutations of n objects, number of permutations of r objects from
a set of n objects.
2
Combinations
ex. How many ways can you pair up 8 boys and 8 girls?
ex. How many distinguishable ”words” can be made from abbaacbb?
Notes:
1
ex. A, B, C, D, and E interviewed for a job. Of the five interviewed, three will be given a job.
The order in which they are selected for the positions does not matter. If S is the sample space
corresponding to this experiment, what is n(S)?
ex. A committee of 15 consists of 8 men and 7 women. How many ways can we form a subcommittee
of 5 people?
If the subcommittee is all female?
If the subcommittee has at least 2 women?
Notes:
2
ex. 20 people are called for jury duty. 12 will be randomly selected for the duty with 3 alternates.
We assume that the order of the alternates matters. How many ways can we select a jury with
alternates?
If the order of the alternates doesn’t matter?
3
Probability applications of counting principles
ex. What is the probability that at least 2 people in this room share a birthday?
ex. A fair coin is tossed 6 times. Find the probability of obtaining exactly 3 heads.
Notes:
3
ex. A bowl contains 6 blueberries and 9 cranberries. If we select two without replacement, what is
the probability that both are cranberries?
What is the probability with replacement?
ex. Assume Texas license plates are 3 letters followed by 4 digits. Your license plate starts with an
M and ends with a digit that is a multiple of 4. What is the probability that a random Texas car
will also have a license plate starting with an M and ending with a digit that is a multiple of 4?
ex. 23 of 30 oranges collected from a tree are ripe. 10 are randomly selected to be given to
neighbors. What is the probability that at least 8 of those we gave to neighbors are ripe?
Notes:
4