In this problem, since the digits can be repeated, you have to know how many possible digit can be used in every digit of a five – digit number. On the first digit of the number, there are 5 possible digits. The second digit of the number has 5 possible digits as well. The third digit of the number has 5 possible digits. The fourth and the fifth digit will have 5 possible digits as well. Multiplying the possible digits for each digit of a five – digit number:
5 x 5 x 5 x 5 x 5 = 3,125 possible five – digit numbers
The number of 5-digit (positive) even numbers can be formed using the given digits, if digits can be repeated is 2500.
Arrangement of the things or object is mean to make the group of them in a systematic order, in all the possible ways.
The number of possible ways to arrange is the n!.
Here, n is the number of objects.
As the even number from the given digits has to find out. Thus the last number of the digit should be even for a even digit.
The number given in the problem are,
4, 6, 7, 2, 8
Here, 4 digits are even, which are,
4, 6, 2, 8
At the first to forth place, there is 5 possible digit can be placed, but at the fifth place, the number of digit can be placed is 4.
The number of 5-digit (positive) even numbers can be formed using the given digits, if digits can be repeated is,
[tex]n=5\times5\times5\times5\times4\\n=2500[/tex]
Thus, the number of 5-digit (positive) even numbers can be formed using the given digits, if digits can be repeated is 2500.
Learn more about the arrangement here;
https://brainly.com/question/6032811
