Question

How many 4-digit numbers are there with no digit repeated?

Answer 1

Hint: Here we have to form a 4-digit number which has to fill hundreds, tens, unit place with any of the 9 digits.

Complete step-by-step answer:
A four digit number is to be formed from the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9.
Since the leftmost place i.e. thousand’s place cannot have zero (because then it would become a 3 digit number).
So, there are 9 ways to fill thousand’s places.
Since, repetition is not allowed, so hundred places can be remaining 9 digits.
So, hundred’s place can be filled in 9 ways.
Similarly, to fill ten’s place, we have 8 digits remaining.
So, ten’s place can be filled by 8 ways.
Similarly, to fill the unit place, we have 7 digits remaining.
So, the unit place can be filled by 7 ways.
So, the required number of ways in which four digit numbers can be formed from the given digits is $$9\times 9\times 8\times 7=4536$$.

Note: In this type of question always calculate the number of ways of filling a particular place and then multiply, you will get your answer. Also remember that zero can’t be placed at the 1000th place of a 4 digit number as it would become a 3 digit number.