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If we list all the numbers that can be generated by the numbers 2, 4, 5, 6, 7, and 8, and arrange
them in the increasing order what position will the number 872456 be placed?
For example, if we consider the numbers that can be generated by the numbers 1, 4, and 5, and
arrange them, we will get the following ordering of the numbers:
1) 145
2) 154
3) 415
4) 451
5) 514
6) 541
We see that 145 is in the first position, 154 is in the second position, and so on

Answer :

Using the arrangements formula, it is found that the number is in position 697.

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The number of possible arrangements of n elements is given by:

[tex]A_n = n![/tex]

In this problem, the numbers are sorted as:

  • Numbers in which the first is not 8.
  • Numbers in which the first is 8, and the second is not 7.
  • 872456 is the first number that starts with 87.

Number of elements which we do not start with 8.

  • For the first digit, there are 5 possible options, which are 2, 4, 5, 6 and 7.
  • For the remaining five, it is arrangement of 5.

Thus:

[tex]n = 5 \times 5! = 600[/tex]

Numbers that start with 8, and the second element is not 7.

  • For the second digit, there are 4 possible options, which are 2, 4, 5 and 6.
  • For the remaining four digits, it is an arrangement of 4.

Thus:

[tex]n_2 = 4 \times 4! = 96[/tex]

Total:

[tex]600 + 96 = 696[/tex]

872456 is the first number which starts with 87, thus it is at position 697.

A similar problem is given at https://brainly.com/question/24648661

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