Question

How many numbers can be formed between 30,000 and 40,000 can be formed with the digits 2,3,5,6,9 if each digit can be repeated any number of times?
A.\[{4^5}\]
B.\[{5^5}\]
C.\[{4^4}\]
D.\[{5^4}\]

Answer 1

Hint: Here the numbers to be formed are from 30,000 to 40,000. That is less than 40,000 and greater than 30,000. So, in the ten thousandth place we cannot put any digit other than 3 because they will be either greater than our required range or will be less than. This is the hint that leads to the problem.

Complete step by step solution:
The problem is based on simple general knowledge we can say. Or in mathematical language we can say it is just checking the combination capacity.
Here given that the digits 2,3,5,6,9 are to be used to form any number between 30,000 and 40,000.
Provided each digit can be repeated any number of times.
But we cannot put any digit other than 3 on the ten thousandth place because they will either lie lower to 30000 or greater than 40000.
So now the digit on the ten thousandth place is fixed. So we will arrange or manage the remaining 4 numbers on their places to form a five digit number. So the possible number will be \[{5^4}\].
So option D is the correct answer.
So, the correct answer is “Option D”.

Note: We will note why the answer is this only and why not the rest.
See options with base 4 are not correct because we are forming a five digit number.
Option B is incorrect because we cannot shift digit 3 anywhere except ten thousandth place neither can we repeat it with other digits.
So option D is the correct one.