Question

How many three digit numbers are there?

Answer 1

Hint: In this question, we have to tell the number of three-digit numbers. For this, we will use the concept of permutation. We will calculate possible digits that can be placed in each place (tens, ones, and hundreds) and then multiply the ways to get our final answer.

Complete step by step answer:
Here we need to tell the number of three-digit numbers. To form a three-digit number, we require three places which are ones, tens, and hundreds. We have a total of 10 digits in the number system i.e. (0, 1, 2, 3, 4, 5, 6, 7, 8, 9). We can place these digits on our three places to get the three-digit number. At one's place, any of the tens digit can be placed. Therefore, the total ways of selecting digits for one’s place will be equal to 10.
At tens place, any of the tens digit can be placed. Therefore, the total ways of selecting digits for tens place will be equal to 9.
Now let us look at hundreds of places. As we can see, we cannot place all 10 digits but we can place only 9 digits because 0 cannot be at hundreds of places, our number becomes a two-digit number which is not required. Therefore, the number of digits that can be placed in hundreds place is 9.
 $ \dfrac{9\text{ ways}}{\text{Hundreds}}\dfrac{10\text{ ways}}{\text{Tens}}\dfrac{10\text{ ways}}{\text{Ones}} $ .
For finding total ways of making numbers, we just need to multiply all the ways for ones, tens, and hundreds. Therefore, total numbers becomes $ 10\times 10\times 9=900 $ .
Hence the total number of three-digit numbers is 900.

Note:
 Students always make mistakes of taking 0 as one of the possibilities for hundreds of places but it is wrong. Sometimes students forget about considering 0 as a digit for ones and tens place also. Make sure to multiply all ways rather than in addition because these events are occurring simultaneously.