Trees and counting techniques
AQM
Champlain College
Exercise 1
Compute the following factorials :
1. 0!
2. 1!
3. 6!
4. 10!
Exercise 2
Compute the following permutations :
1. P7,5
2. P4,4
3. P9,9
Exercise 3
Compute the following combinations:
1. C5,3
2. C8,5
3. C2,2
1
Exercise 4
There are 11 qualified applicants for 7 trainee positions in a fast-food management program. How many different groups of trainees can be selected?
Exercise 5
1. Draw a tree diagram to display all the possible head-tail sequences that
can occur when you flip a coin three times
2. How many outcomes contain a head and a number greater than 4?
3. Probability extension: Assuming the outcomes displayed in the tree diagram are all equally likely, what is the probability that you will get a head
and a number greater than 4 when you flip a coin and toss a die? (Round
your answer to three decimal places.)
.
Exercise 6
A sales representative must visit six cities. There are direct air connections
between each of the cities. Determine the number of different choices the sales
representative has for the order in which to visit the cities.
Exercise 7
1. Draw a tree diagram to display all the possible outcomes that can occur
when you flip a coin and then toss a die.
2. How many outcomes contain a head and a number greater than 4?
3. Assuming the outcomes displayed in the tree diagram are all equally likely,
what is the probability that you will get a head and a number greater than
4 when you flip a coin and toss a die? (Round your answer to three decimal
places.)
2