Download Counting Techniques using Cases

Counting Techniques using Cases
1. How many binary sequences of length 6,7 or 8 begin with 0?
2. How many three digit numbers can be created from the digits 1 through 9 if replacement if
not allowed? How many three digit numbers can be created from the digits 0 through 9 if
replacement is not allowed? How does the values change if replacement is allowed?
3. A PIN number for a photocopier can be any sequence of three or four digits.
a) How many such PIN number are there?
b) What is the probability that your PIN, given to you at random, will start with a 2?
c) What is the probability that your PIN, given to you at random, will contain at least one 2?
4. A six digit integer is formed by selecting digits from the set {1,2…, 9} without replacement.
How many are less than 460 000?
5. There are 5 men and 6 women that are available to be chosen to form a 5 member
committee for market research. If this group was selected at random, what is the
probability that this committee will have:
a) Exactly three women?
b) At least three women?
c) At least one man?
6. A cable contains 12 wires that are colour coded. There are three green, three red, three
black and three white wires. If four wires are picked at random what is the probability that:
a) there is exactly one green wire?
b) There is exactly one of each colour?
c) At least one green wire is selected?
d) At least two green wires are selected?
e) Two green and two red are selected?
f) Exactly two different colours are selected?