How many numbers lying between 100 and 1000 can be formed, (i) if the repetition of the digits isn't allowed? (ii) if the repetition of digits is allowed?
1 Answer
Dec 25, 2017
648 with no repetition. 899 with repetition.
Explanation:
I'm going to assume that when we say "lying between" that the numbers 100 and 1000 are excluded.
We are looking at the numbers 101 through 999, which is
If repetition of digits is allowed, then we can make all 899 numbers.
If repetition of digits isn't allowed, then we can look at it this way:
We can pick any digit from 1 to 9 to be the first digit - that's 9 choices.
We can pick any of 9 digits for the second digit (that's 0 to 9 except for what was picked for the first digit).
We can pick any of 8 digits for the third digit (that's 0 to 9 except for the two digits picked previously). That gives:
