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CHIU,
Probabilistic Analysis: Structuring, Processing and Communicating Probabilistic Information
10
Exercises
Chapter 2
1.
The New California Super Lotto picks five distinct numbers from 1 to 47, and
another
number (possibly identical to one of the earlier chosen five) from 1 to 27.
Compute the
number of possible winning combinations – more than double from the old game
(which was to choose six distinct numbers from 1 to 52).
2.
We have nine flags, 4 of which are white, 3 red, and two blue.
How many different
linear color arrangements of the nine flags can be made if flags from the same color are
identical (thus undistinguishable)?
3.
2 Republicans, 2 Democrats and 3 Independents need to be chosen to form a committee
of 7 members from a group of 5 Republicans, 6 Democrats and 4 Independents.
How
many different committees are possible?
4.
Kara has ten books which she wants to place in her (single shelf) bookshelf arranged by
subject.
She has 4 probability books, 3 optimization books, 2 decision analysis books
and 1 economic book.
In how many ways can she arrange her books?
5.
If eight identical blackboards are to be divided among 4 schools, how many divisions
are possible?
What if each school must receive at least one blackboard?
6.
Paul wants to invite 5 out of 8 friends to a tea party.
How many possible guest lists can
be created (the ordering in each list does not matter), if:
(a)
2 friends are feuding and don't want to attend together.
(b)
2 friends will only attend if both are invited.
7.
A student taking a test has to select 7 out of 10 questions.
How many different choices
does she have if:
(a)
There are no other restrictions?
(b)
She has to answer exactly 2 of the last 4?
(c)
She has to answer exactly 2 of the first 6?
(d)
She has to answer at least 3 of the first 5?
8.
A bone marrow transplant can be made only between two people with all six human
leukocyte antigens (HLA) being compatible.
Each person's halotype consists of 2
HLAA antigens, 2 HLAB antigens, and 2 HLADR antigens.
There are a total of 18,
40, and 14 HLA antigens for types A, B, and DR, respectively.
The order of the
antigens is irrelevant and the antigens in each type can be repeated.
How many
possible antigen strings are there?
9.
Six tourists decide to split into three groups of two to take care of three activities:
rent
a van, get the luggage, and make hotel reservations.
How many possible divisions are
possible?
The same 6 tourists decide to take it easy the first night and stay in the hotel
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Probabilistic Analysis: Structuring, Processing and Communicating Probabilistic Information
11
Exercises
to play Pictionary.
They need to split into two groups of three each.
How many
divisions are possible?
10.
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This document was uploaded on 10/01/2010.
 Fall '09

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