How many three digit numbers have three distinct digits?
1st digit: 9 choices
2nd digit: 9 choices
3rd digit: 8 choices
so, 9*9*8
Actually not because the problem is asking for 3 digits such as 100
Sorry made a mistake you are right
To find the number of three-digit numbers with three distinct digits, we can break down the problem into three steps:
Step 1: Choose the hundreds digit:
Since we need three distinct digits, we can choose any digit from 1 to 9 (excluding 0) as the hundreds digit. So, we have 9 choices for the hundreds digit.
Step 2: Choose the tens digit:
After choosing the hundreds digit, we cannot reuse that digit. So, we have 9 remaining digits to choose from (as we already used one for the hundreds digit). Hence, we have 9 choices for the tens digit.
Step 3: Choose the units digit:
Similarly, after choosing the hundreds and tens digit, we cannot reuse those digits. So, we have 8 remaining digits to choose from. Hence, we have 8 choices for the units digit.
Now, we multiply the number of choices in each step together to get the total number of three-digit numbers with three distinct digits:
Number of three-digit numbers = (Number of choices for hundreds digit) x (Number of choices for tens digit) x (Number of choices for units digit)
Number of three-digit numbers = 9 x 9 x 8 = 648
Therefore, there are 648 three-digit numbers with three distinct digits.