With reference to Exercise 1, suppose that there is athird step, and if the first step is made in the ith way andthe second step in the jth way, the third step can be madein n3ij ways.(a) Use a tree diagram to verify that the whole operationcan be made in n1i=1n2ij=1n3ij different ways. (b) With reference to part (b) of Exercise 1, use the for-mula of part (a) to verify that there are 32 ways in which the student can study at most 4 hours for the test on threeconsecutive days.
With reference to Exercise 1, suppose that there is athird step, and if the first step is made in the ith way andthe second step in the jth way, the third step can be madein n3ij ways.(a) Use a tree diagram to verify that the whole operationcan be made in n1i=1n2ij=1n3ij different ways. (b) With reference to part (b) of Exercise 1, use the for-mula of part (a) to verify that there are 32 ways in which the student can study at most 4 hours for the test on threeconsecutive days.
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter2: Systems Of Linear Equations
Section2.4: Applications
Problem 32EQ
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Question
With reference to Exercise 1, suppose that there is a
third step, and if the first step is made in the ith way and
the second step in the jth way, the third step can be made
in n3ij ways.
(a) Use a tree diagram to verify that the whole operation
can be made in
n1
i=1
n2i
j=1
n3ij
i=1
n2i
j=1
n3ij
different ways.
(b) With reference to part (b) of Exercise 1, use the for-
mula of part (a) to verify that there are 32 ways in which
mula of part (a) to verify that there are 32 ways in which
the student can study at most 4 hours for the test on three
consecutive days.
consecutive days.
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