How many different three-digit numbers can be written using digits from the set of 1, 2, 3, 4,5 without any repeating digits?
5x4x3 different three-digit numbers
To find the number of different three-digit numbers that can be written using digits from the set {1, 2, 3, 4, 5} without any repeating digits, you can use the concept of permutations.
Permutations are arrangements of objects where the order matters and no repetition is allowed. In this case, we want to find the number of permutations of three distinct digits chosen from the set {1, 2, 3, 4, 5}.
To calculate the number of permutations, follow these steps:
Step 1: Determine the number of choices for the first digit. Since there are five digits in the set {1, 2, 3, 4, 5}, the first digit can be chosen from any of these five.
Step 2: After choosing the first digit, there are four remaining digits available for the second digit. So the second digit can be chosen from the remaining four digits.
Step 3: Once the first and second digits are chosen, there are three remaining digits available for the third digit.
Therefore, the total number of different three-digit numbers that can be formed without any repeating digits is:
Number of choices for first digit × Number of choices for second digit × Number of choices for third digit = 5 × 4 × 3 = 60
So, there are 60 different three-digit numbers that can be written using digits from the set {1, 2, 3, 4, 5} without any repeating digits.
To find the number of different three-digit numbers that can be written using digits from the set of 1, 2, 3, 4, 5 without any repeating digits, we can use the concept of permutations.
In this case, we have 5 options for the first digit (1, 2, 3, 4, or 5), 4 options for the second digit (as we cannot repeat the digit used for the first digit), and 3 options for the third digit (as we cannot repeat any of the previously used digits).
Using the formula for permutations,
nPr = n! / (n-r)!
where n is the total number of options and r is the number of options we choose at a time, we can calculate the total number of three-digit numbers.
Applying the formula:
5P3 = 5! / (5-3)!
= 5! / 2!
= (5 x 4 x 3 x 2 x 1) / (2 x 1)
= (120) / (2)
= 60
Therefore, there are 60 different three-digit numbers that can be written using digits from the set of 1, 2, 3, 4, and 5 without any repeating digits.