Respuesta :
Four digit number can be formed using 0,1,2,3,4,5,6,7,8,9
Any number which ends with 0 or 5 is divisible by 5.
_ _ _ _ We have to check for 4 digit numbers. The 4 digit number must end with 0 or 5.
So the number at the thousandth place can be written in 9 ways (since 0 can not be written at thousandth place) = 9
the number at the hundredth place can be written in 10 ways = 10
the number at the tenth place can be written in 10 ways = 10
the number at the unit place can be written in 2 ways = 2
So the number of ways the 4 digit number can be written as (9)(10)(10)(2) = 1800 ways.
For total number of ways:
the number at the thousandth place can be written in 9 ways = 9
the number at the hundredth place can be written in 10 ways = 10
the number at the tenth place can be written in 10 ways = 10
the number at the unit place can be written in 10 ways = 10
Total number of ways = (9)(10)(10)(10) = 9000 ways
So the number of ways the 4 digit number can be written that can be divisible by 5 = Total number of ways - number of ways the 4 digit number can be written
The number of ways the 4 digit number can be written that can be divisible by 5 = 9000 - 1800 = 7200 ways
7200 four-digit numbers cannot be divided by 5.
We have the numbers 0,1,2,3,4,5,6,7,8,9
What is permutation?
A Permutation is the arrangement of things.
In order to make a number not divisible by 5 its unit digit must not be 0 and 5.
So, the number of ways to fill the unit place of a 4 digit number = all digits except 0 and 5 i.e. 8 ways
The number of ways to fill the thousand place of a 4 digit number =all digits except 0 i.e 9 ways
The number of ways to fill the hundredth place of a 4 digit number =10 ways
The number of ways to fill the tenth place of a 4 digit number =10 ways
So, the total number of ways to make a 4 digit number not divisible by 5
= 8*9*10*10
=7200 ways.
Hence, 7200 four-digit numbers cannot be divided by 5.
To get more about permutations visit:
https://brainly.com/question/12468032
