Question

You have the following digits 4, 5, 6, 0, 7 and 8. Using them, make five numbers each with 6 digits.
Arrange them in ascending and descending order.

Answer 1

Hint: Ascending order means arranging the digits in increasing order like for example 222, 234, 245, 278, 289 are in ascending order and descending order means arranging the terms in decreasing order 289, 278, 245, 234, 222 are in descending order.

Complete step-by-step answer:
Before proceeding with the question we must know how to form the numbers using digits and what is ascending and descending orders.
In order to arrange a set of given numbers in ascending order, we have to place the number that has the least value first and then the next number that has higher value after it and continue till the number having the highest value. In order to arrange a set of given numbers in descending order, we have to place the number that has the highest value first and then the next number having least value after it and continue till the number having the least value.
In this question we have been given the following digits 4, 5, 6, 0, 7 and 8. Using them, we have to make five numbers, each with 6 digits and then arrange them in ascending and descending order.
Let us first form six digit numbers using the given digits i.e. 4, 5, 6, 0, 7 and 8.
The six digit numbers can be formed by just placing all given six digits and then we can interchange any of the numbers from its place to form new numbers.
We have to form five numbers, therefore, let us form the six digits numbers as:
456078, 870564, 607854, 478605, 786054
Using the knowledge of ascending order, the lowest number here is 456078, so that comes first. Then, we have 478605 next to it. Going on with all the numbers, finally, we will get the ascending order as:
456078, 478605, 607854, 786054, 870564
Using the knowledge of descending order, the highest number here is 870564, so that comes first. Then, we have 786054 next to it. Going on with all the numbers, finally, we will get the descending order as:
870564, 786054, 607854, 478605, 456078
Hence, the five six digits number formed by the given digits are:
456078, 870564, 607854, 478605, 786054
Ascending order is - 456078, 478605, 607854, 786054, 870564
Descending order is - 870564, 786054, 607854, 478605, 456078

Note: We must be very careful while arranging the numbers in ascending and descending orders. While forming the numbers, we must be very careful while using the digits. Sometimes, we might end up forming the numbers with the same digits placed twice. This can lead us to the wrong answers as nothing is said about repetition of the given digits in the question.