How many different whole numbers can be made with the digits 5, 7, 8? For this problem, each different whole number may have 1, 2, or 3 digits and a digit may be repeated.
12
To determine the number of different whole numbers that can be made with the digits 5, 7, and 8, we need to consider different cases based on the number of digits.
Case 1: Single-digit numbers
Since we are allowed to repeat digits, there are three possible single-digit numbers: 5, 7, and 8.
Case 2: Two-digit numbers
To find the number of two-digit numbers, we can consider all possible combinations of the three given digits. This is calculated using the formula for combinations, nCr, where n is the total number of options and r is the number of items chosen at a time.
In this case, we need to find the combinations of 3 digits taken 2 at a time, which is denoted as 3C2. Using the formula, 3C2 = 3! / (2! * (3-2)!) = 3.
Therefore, there are three possible two-digit numbers: 57, 58, and 78.
Case 3: Three-digit numbers
To find the number of three-digit numbers, we can use the same approach as in the previous case. We need to find the combinations of 3 digits taken 3 at a time, which is denoted as 3C3. Using the formula, 3C3 = 3! / (3! * (3-3)!) = 1.
Therefore, there is one possible three-digit number: 578.
Lastly, we sum up the results from each case:
Single-digit numbers: 3
Two-digit numbers: 3
Three-digit numbers: 1
The total number of different whole numbers that can be made with the digits 5, 7, and 8 is 3 + 3 + 1 = 7.