How many natural numbers are there from $1$ to $1000$ which have none of their digits repeated?
Hint: We have 3 kinds of digits from $1$ and $1000$ such as one digit numbers, two digit numbers and three digit numbers.
Now here we have to find natural numbers where none of the digits should be repeated. Here from $1$ to $1000$ we have $3$ kinds of digits One digit numbers, two digit numbers and three digit numbers.
One digit numbers: We know that there are $9$ possible to get single digit numbers from $1 - 9$ $ \Rightarrow 9 ways$ Two digit numbers: Here the first digit can be from $1 - 9$ and the second digit can be from$0 - 9$. We also know that “zero” cannot be the first digit so we have excluded it Total possible = $9 \times 9 = 81$ ways Three digit numbers: Here the first digit can be from $1 - 9$ and the second digit can be from $0 - 9$ but not the first digit $10 - 1 = 9$. And the third digit can be from $0 - 9$ but not the same as the first and second digit. Total possible=$9 \times 9 \times 8 = 648$
Here we have found all the possible under without repetition condition Therefore total number of natural numbers from $1$ to $1000$ without repetition=$648 + 81 + 9 = 738ways$.
Note: Make a note that digits should not be repeated and kindly focus that zero can’t be the first digit for any kind terms.
Sorry!, This page is not available for now to bookmark.