Introduction :
Fundamental principle of counting states that “if an event can occur in m different ways, following which another event can occur in n different ways, then the total number of occurrence of the events in the given order is m x n.” Let us find the number of 4 letter words, with or without meaning that can be formed out of the letters from the word ROSE, where we could repeat the letters. Since we have to find 4 letter words, draw 4 squares `square square square square` . Keep in mind that repetition is not allowed. The first place can be filled in 4 different ways and the remaining three letters in three different ways, following which the third place can be filled in 2 different ways; following which, the fourth place can be filled in 1 way. Thus, the number of ways in which the 4 places can be filled, by the multiplication principle, is 4 x 3 x 2 x 1 = 24. Hence, the required number of words is 24.Here we can see teh definition of permutation.
Permutation and Definition of Permutation:
In the above example, we are actually counting the different possible arrangements of the letters such as ROSE, ROES, SOER,… etc. Here, in this list, each arrangement is different from the other. In other words, the order of writing the letters is important. Each arrangement is called a permutation of 4 different letters taken at a time. Now, if we have to determine the number of 3 letter words, with or without meaning, which can be formed out of the letters of the word NUMBER, where the repetition of the letters is not allowed, we need to count the arrangements NUM, NMU, MUN,…etc. Here, we are counting the permutations of 6 different letters taken 3 at a time. Required number of words = 6 x 5 x 4 = 120.
Definition of Permutation:
A permutation is an arrangement in a definite order of a number of objects taken some or all at a time.
Formula for nPr = `(n!)/((n-r)!), 0<=r<=n`
Fundamental principle of counting states that “if an event can occur in m different ways, following which another event can occur in n different ways, then the total number of occurrence of the events in the given order is m x n.” Let us find the number of 4 letter words, with or without meaning that can be formed out of the letters from the word ROSE, where we could repeat the letters. Since we have to find 4 letter words, draw 4 squares `square square square square` . Keep in mind that repetition is not allowed. The first place can be filled in 4 different ways and the remaining three letters in three different ways, following which the third place can be filled in 2 different ways; following which, the fourth place can be filled in 1 way. Thus, the number of ways in which the 4 places can be filled, by the multiplication principle, is 4 x 3 x 2 x 1 = 24. Hence, the required number of words is 24.Here we can see teh definition of permutation.
Permutation and Definition of Permutation:
In the above example, we are actually counting the different possible arrangements of the letters such as ROSE, ROES, SOER,… etc. Here, in this list, each arrangement is different from the other. In other words, the order of writing the letters is important. Each arrangement is called a permutation of 4 different letters taken at a time. Now, if we have to determine the number of 3 letter words, with or without meaning, which can be formed out of the letters of the word NUMBER, where the repetition of the letters is not allowed, we need to count the arrangements NUM, NMU, MUN,…etc. Here, we are counting the permutations of 6 different letters taken 3 at a time. Required number of words = 6 x 5 x 4 = 120.
Definition of Permutation:
A permutation is an arrangement in a definite order of a number of objects taken some or all at a time.
Formula for nPr = `(n!)/((n-r)!), 0<=r<=n`
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