Answer:
1364 is the number of possibilities for positive integers less than 1,00,000.
Explanation:
1. 5 digit numbers:
We have 5 places here, and each place can have 4 options because repetition is allowed.
So, total number of possibilities for 5 digit numbers:
2. 4 digit numbers:
We have 4 places here, and each place can have 4 options because repetition is allowed.
So, total number of possibilities for 4 digit numbers:
3. 3 digit numbers:
We have 3 places here, and each place can have 4 options because repetition is allowed.
So, total number of possibilities for 3 digit numbers:
4. 2 digit numbers:
We have 2 places here, and each place can have 4 options because repetition is allowed.
So, total number of possibilities for 2 digit numbers:
5. 1 digit numbers:
We have 1 place here, and each place can have 4 options because repetition is allowed.
So, total number of possibilities for 1 digit numbers:
We can add all the above possibilities to find the total.
So, number of positive integers less than 100,000 whose digits are among 1, 2, 3, and 4 = 1024 + 256 + 64 + 16 + 4 = 1364