the number of positive integers less than 40000 that can be formed using all the digits 12345 is equal to
The first digit must be 1,2 or 3
That leaves 4 digits to shuffle for the others.
So, the total number is
3 * 4! = 72
To find the number of positive integers less than 40000 that can be formed using all the digits 12345, we need to consider a few conditions:
1. Each number must be a positive integer less than 40000.
2. Each number must be formed using all the digits 1, 2, 3, 4, and 5.
To solve this problem, we can break it down into smaller steps:
Step 1: Count the number of permutations of the digits 1, 2, 3, 4, and 5.
The number of permutations is given by the factorial of the number of digits, which in this case is 5.
5! = 5 x 4 x 3 x 2 x 1 = 120
So, there are 120 different permutations of the digits 1, 2, 3, 4, and 5.
Step 2: Determine the range of numbers we need to consider.
Since we are looking for positive integers less than 40000, we need to find the highest number that can be formed using the given digits.
The highest number would be 54321.
Step 3: Count the number of valid numbers.
To find the number of valid numbers, we need to consider all the permutations and exclude any numbers greater than 40000.
From step 1, we know that there are 120 different permutations.
Starting with the highest permutation (54321) and going in descending order, we can count how many of these permutations are valid, i.e., less than 40000.
54321 -> Not valid (greater than 40000)
54312 -> Not valid (greater than 40000)
...
12345 -> Valid
We can count the number of valid numbers as we go down the list of permutations until we reach the first valid number less than 40000.
If we count the valid permutations, we find that there are 24 valid numbers.
So, the number of positive integers less than 40000 that can be formed using all the digits 12345 is equal to 24.