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THE FUNDAMENTAL PRINCIPLE OF ASSOCIATION
The lemma stated below is known as the fundamental principle of association.
Lemma:
Example:
Solution:
Lemma:
Suppose if one operation can be performed in m ways and after it has been
performed in any of these ways, a second operation can be performed in n
ways, then the total number of ways of performing the two operations will
be m x n.
Example:
Three families went out for a tour and arrived in a hotel. There are 5 vacant
rooms in the hotel. In how many ways can the families take up their quarters,
each in different room?
Solution:
Clearly, the first family can choose any one of the 5 different rooms; hence
this family has 5 different selections and when it has made its selection in
any one way, the second family will have a choice of 4. Then, the first two
families can select their rooms in 5 x 4 ways. Again, with any one choice of
the first two, the third family can select their rooms in 3 ways. Hence, the
three families can select their rooms in 5 x 4 x 3 = 60 ways.
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