Question

Use the given digits without repetition and make the greatest and smallest 4-digit numbers.
$
  2 \\
  8 \\
  7 \\
  4 \\
 $

Answer 1

Hint: In order to solve the given question, we will look for different permutation and combination substituting each digit in different places in order to find the greatest and smallest 4 digit number without repetition. We will take the help of ascending and descending order of the digits in order to for the number which is largest and smallest amongst all.

Complete step-by-step answer:
Given digits are: 2,8,7,4
First let us make the largest four digit number without repetition.
In order to make the largest 4 digit number the thousands place must have the largest digit followed by hundreds and tens place.
So we will first need to arrange the numbers in descending order before using them.
Arranging the given numbers in descending order:
8,7,4,2
So arranging them from largest to lowest we have: 8,7,4,2
Therefore, greatest number without repetition: 8742

Now let us make the smallest four digit number without repetition.
In order to make the smallest 4 digit number the thousands place must have the smallest digit followed by hundreds and tens place.
So we will first need to arrange the numbers in ascending order before using them.
Arranging the given numbers in ascending order:
2, 4, 7, 8
So arranging them from smallest to largest we have: 2, 4, 7, 8
Therefore, smallest number without repetition: 2478

Hence, the greatest and smallest 4-digit numbers without repetition are 8742 and 2478 respectively.

Note: The key in solving such types of problems is to understand the meaning of ascending and descending order.
Ascending order means the numbers are arranged from smallest to largest increasing.
Descending order means the numbers are arranged from largest to smallest decreasing.