Chapter 13.2, Problem 22PPS

(a)

To determine

To Find: The possible permutation of the three integers.

Answer to Problem 22PPS

The permutations are $382,328,238,283,832,823$ .

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 $382,328,238,283,832,823$ .

(b)

To determine

To Find: The complete form for the given table.

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	$382,328,238,283,832,823$	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 determine

To Find: The conjecture about the value of the average of the permutations of the three digits between 0 and 9.

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 determine

To Find: Whether is it possible to write and equation for the average of the permutation of the digits.

Answer to Problem 22PPS

The average of the permutation of the three integers is $37\left(x+y+z\right)$ .

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 $x,y,z$ and the average of the permutation of the three integers is $37\left(x+y+z\right)$ .