How many different 3 digit numbers less than 500 can be made using the digits 3, 4, 5, and 6 if the digits can be used only once
However, not all of those numbers are less than 500.
choices for 1st digit: 2 (3 or 4)
choices for 2nd digit: 3
choices for 3rd digit: 2
so, there are really only 12 possible numbers less than 500
To find the number of different 3-digit numbers that can be made using the digits 3, 4, 5, and 6, we need to break down the problem step-by-step:
Step 1: Determine the possible choices for the hundreds place.
Since we need to find numbers less than 500, the only possible choice for the hundreds place is 3.
Step 2: Determine the possible choices for the tens place.
For the tens place, we have three digits available: 4, 5, and 6.
Since we cannot repeat digits, we have three choices for the tens place.
Step 3: Determine the possible choices for the ones place.
Again, we have three digits available: 4, 5, and 6.
However, one of the choices has already been used in the tens place, so we have two choices for the ones place.
Step 4: Calculate the total number of possibilities.
To calculate the total number of possibilities, we need to multiply the number of choices at each step.
Number of choices for the hundreds place = 1 (3)
Number of choices for the tens place = 3
Number of choices for the ones place = 2
Total number of possibilities = number of choices for the hundreds place × number of choices for the tens place × number of choices for the ones place
= 1 × 3 × 2
= 6
Therefore, there are 6 different 3-digit numbers less than 500 that can be made using the digits 3, 4, 5, and 6, with each digit used only once.
To determine the number of different 3-digit numbers that can be made using the digits 3, 4, 5, and 6, we can use a combination of counting principles.
First, we need to figure out the possibilities for the hundreds digit. Since we want numbers less than 500, the hundreds digit can only be either 3 or 4. So, we have two choices for the hundreds digit.
Next, let's move on to the tens digit. Once we choose the hundreds digit, we are left with three remaining digits: 4, 5, and 6. Since each digit can only be used once, after we select the hundreds digit, we will have three digits left to choose from for the tens digit. Therefore, there are three choices for the tens digit.
Finally, we move on to the units digit. After we have chosen the hundreds and tens digits, we are left with two remaining digits. Again, each digit can only be used once, so there are two choices for the units digit.
Now, to find the total number of different 3-digit numbers, we multiply the number of choices for each digit together. In this case, we have:
Number of choices for hundreds digit: 2
Number of choices for tens digit: 3
Number of choices for units digit: 2
Total number of different 3-digit numbers = 2 * 3 * 2 = 12
Therefore, there are 12 different 3-digit numbers less than 500 that can be made using the digits 3, 4, 5, and 6, where each digit can only be used once.
Number of choices for the first digit = 4
Since there cannot be repetitions,
Number of choices for the second digit = 3
similarly,
Number of choices for the third digit = 2
By the multiplication principle, the number of different 3-digit numbers with distinct digits that can be made from 4
= 4*3*2 = ?