How many integers between 1000 and 10000 have no digits other than 4, 5 or 6?Choices:- 81 91 51 61
Question
How many integers between 1000 and 10000 have no digits other than 4, 5 or 6?
Choices:
- 81
- 91
- 51
- 61
Solution
To solve this problem, we need to consider the number of digits in the integers between 1000 and 10000.
-
For a 4-digit number, each digit can be either 4, 5, or 6. So, there are 3 options for each of the 4 digits. Therefore, the total number of 4-digit numbers with these digits is 3^4 = 81.
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For a 5-digit number, it can't be more than 10000, so the first digit can only be 1, which is not allowed in this problem. Therefore, there are no 5-digit numbers that meet the criteria.
So, the total number of integers between 1000 and 10000 that have no digits other than 4, 5, or 6 is 81.
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