how many numbers greater than 100 can be formed using the digits 1,2,3,4,5,if no digits may be repeated.
Your numbers could be either 3 digits, 4 digits or all 5 digits
3 digits: 5*4*3 = 60
4 digits: 5*4*3*2 = 120
5 digits: 5*4*3*2*1 = 120
total = ...
To find the number of numbers greater than 100 that can be formed using the digits 1, 2, 3, 4, 5 without any repetition, we can break it down into steps:
Step 1: Select the first digit:
Since the number has to be greater than 100, the first digit cannot be 1. Therefore, we have 4 choices: 2, 3, 4, or 5.
Step 2: Select the second digit:
Since no digits can be repeated, there are remaining 4 digits to choose from after selecting the first digit. Therefore, we have 4 choices for the second digit.
Step 3: Select the third digit:
Similarly, there will be 3 choices left after selecting the first two digits.
Step 4: Multiply the choices:
To find the total number of numbers that can be formed, we multiply the number of choices for each step: 4 choices for the first digit × 4 choices for the second digit × 3 choices for the third digit.
4 × 4 × 3 = 48
Therefore, there are 48 numbers greater than 100 that can be formed using the digits 1, 2, 3, 4, 5 without repeating any digit.
To find the number of numbers greater than 100 that can be formed using the digits 1, 2, 3, 4, and 5 without repetition, we can break down the problem into steps:
Step 1: Determine the number of choices for the hundreds place.
Since we need to form numbers greater than 100, the hundreds place can only be filled with the digits 2, 3, 4, or 5. So, there are 4 choices for the hundreds place.
Step 2: Determine the number of choices for the tens place.
Once the hundreds place has been chosen, we can use any remaining digit from the set of 1, 2, 3, 4, and 5 for the tens place. Since we have already used one digit, there are now 4 digits remaining. So, there are 4 choices for the tens place.
Step 3: Determine the number of choices for the units place.
After filling the hundreds and tens places, we will have used two digits, and there will be 3 remaining digits. Therefore, there are 3 choices for the units place.
Step 4: Calculate the total number of possible numbers.
To find the total number of possible numbers, we need to multiply together the number of choices for each place. So, the total number of numbers greater than 100 that can be formed is:
Total numbers = Number of choices for hundreds place × Number of choices for tens place × Number of choices for units place
= 4 × 4 × 3
= 48
Therefore, there are 48 numbers greater than 100 that can be formed using the digits 1, 2, 3, 4, and 5 without repetition.