Assignment
1. A general is planning to invade towns A, B, and C and has 20 soldiers at his
disposal (6 officers and 14 privates). After some thought, the general decides to
select 12 soldiers to carry out the invasion and to keep the remaining 8 (and
himself) behind to protect the command post.
a) If the general selects the 12 soldiers randomly, and without replacement, what is the
probability that 3 will be officers and 9 will be privates?
b) If the general now takes the 12 selected soldiers (3 officers and 9 privates) and
randomly selects 4 soldiers (without replacement) to invade each of towns A, B, and C,
what is the probability that exactly 1 officer ends up being sent to each town?
2. A project director runs a staff consisting of 6 scientists and 3 lab technicians. Three new
projects have to be worked on and the director decides to assign 4 of her staff to the first
project, 3 to the second, and 2 to the third. In how many ways can this be accomplished
if:
a) The director assigns her staff to the projects randomly?
b) Each project requires 1 lab technician?
c) Of the 4 people assigned to the first project, at least 3 are scientists?
3. Ten officers and 10 regular soldiers are going to be assigned to units of size 4, 6,
and 10 to carry out different missions. If assignment is done at random, what is
the probability that each unit will end up being half officers and half regular
soldiers?
4. Each week, Bob and three friends from work pool their money together and buy
12 lottery tickets that are randomly and equally divided up among the group.
a) How many ways can the tickets be divided up among Bob and his friends?
b) By an incredible stroke of luck, this week there are two winning tickets among the 12
tickets purchased by Bob and his friends. What is the probability that different people
end up with these winning tickets?
c) In Lotto Mania, the game played by Bob and his friends, six winning numbers are
selected by random sampling without replacement from a bin of balls numbered 1
through 30. A player wins if the six numbers on his/her ticket match at least five
numbers from the six winning numbers (order is irrelevant). If you buy a single ticket,
what is the probability that you will win something?
5. A sales company purchases 15 new cars for its top salespeople: 6 identical
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