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Considering the definition of permutation, in 5040 ways can the letters in the word ''PAYMENT'' be arranged if the letters are taken 6 at a time.
<h3>What is Permutation</h3>Permutation is placing elements in different positions. So, permutations of m elements in n positions are called the different ways in which the m elements can be arranged occupying only the n positions.
That is, permutations refer to the action of arranging all the members of a set in some sort of order or sequence.
In other words, permutations (or Permutations without repetition) are ways of grouping elements of a set in which:
- take all the elements of a set.
- the elements of the set are not repeated.
- order matters.
To obtain the total of ways in which m elements can be placed in n positions, the following expression is used:
where "!" indicates the factorial of a positive integer, which is defined as the product of all natural numbers before or equal to it.
<h3>This case</h3>In this case, you have:
- the letter word "PAYMENT", where the number of letters is 7.
- the letters are taken 6 at a time.
Then, you know that:
- m= 7
- n=6
Replacing in the definition of permutation:
Solving:
<u><em>7P6= 5040 </em></u>
Finally, in 5040 ways can the letters in the word ''PAYMENT'' be arranged if the letters are taken 6 at a time.
Learn more about permutation:
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