Difference between fundamental theorem of multiplication and addition
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According to my book:
1.The fundamental principle of counting is used to count the number of possible ways in which a task can be done without actually counting manually.
2.Under the fundamental principle of counting comes the principle of addition and the principle of multiplication.
3.The principle of addition states if a one task can be one done in $m$ ways and another task which is MUTUALLY EXCLUSIVE of the first task can be done in $n$ ways, then the the number of possible ways in which either can be done is $m+n$.This result can be generalized.
4.The principle of multiplication states that if one task can be done in $m$ ways and another task which is INDEPENDENT of the first task can be done in $n$ ways, after the first task has been performed, then the number of possible ways in which both the tasks can be done is $m \times n$.This result can be generalized.
5.Permutations refer to the possible arrangements of a collection of objects.
6.Combinations refer to the possible selections of a collection of objects.
1.The fundamental principle of counting is used to count the number of possible ways in which a task can be done without actually counting manually.
2.Under the fundamental principle of counting comes the principle of addition and the principle of multiplication.
3.The principle of addition states if a one task can be one done in $m$ ways and another task which is MUTUALLY EXCLUSIVE of the first task can be done in $n$ ways, then the the number of possible ways in which either can be done is $m+n$.This result can be generalized.
4.The principle of multiplication states that if one task can be done in $m$ ways and another task which is INDEPENDENT of the first task can be done in $n$ ways, after the first task has been performed, then the number of possible ways in which both the tasks can be done is $m \times n$.This result can be generalized.
5.Permutations refer to the possible arrangements of a collection of objects.
6.Combinations refer to the possible selections of a collection of objects.
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