
Concept explainers
(a)
To Find: The possible permutation of the three integers.
(a)

Answer to Problem 22PPS
The permutations are
Explanation of Solution
Given:
The three digits are selected randomly from 0 to 9.
Calculation:
The example for the three digits randomly selected from the integers 0-9 is 3,8, and 2. Thus there are 3!=6 possible permutations of the three integers for the integers 3,8,2.
Then, the permutation are
(b)
To Find: The complete form for the given table.
(b)

Answer to Problem 22PPS
The required table is shown in Table 2
Explanation of Solution
Given:
The given table is shown in Table 1
Table 1
Integers | Permutations | Average of Permutations | Average of permutations 37 |
1,4,7 | 147,174,417,471,714,714, | 444 | 12 |
Calculation:
The first step is to select four integers from 0 to 9 and make the table that list the integersfor given parameters.
The required table is shown in Table 2
Table 2
Integers | Permutations | Average of Permutations | Average of permutations/37 |
1,4,7 | 147,174,417,471,714,714, | 444 | 12 |
3,8,2 | | 481 | 13 |
0,5,4 | 054,045,450,405,504,540 | 333 | 9 |
9,7,1 | 971,917,719,791,197,179 | 629 | 17 |
3,9,6 | 963,936,693,639,396,369 | 666 | 18 |
(c)
To Find: The conjecture about the value of the average of the permutations of the three digits between 0 and 9.
(c)

Answer to Problem 22PPS
The sum of every value in each of the permutation multiplied by 37 is equal to the average value of the all the possible permutations.
Explanation of Solution
From the table shown in table 2 the permutation of the three integers between 0-9 the conjecture that is made is that the sum of every value in each of the permutation multiplied by 37 is equal to the average value of the all the possible permutations.
(d)
To Find: Whether is it possible to write and equation for the average of the permutation of the digits.
(d)

Answer to Problem 22PPS
The average of the permutation of the three integers is
Explanation of Solution
Since, the average of all the possible permutation of the integers from 0-9 is equal to the sum of the integers multiplied by 37 then the integers are represented by the sum
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