Question
How many numbers can be formed using the digits $0,1,2,3,4,5$ without repetition so that the resulting numbers are between 100 and 1000 ?

Answer

A number between 100 and 1000 is a 3 digit number and is to be formed from the digits $0,1,2,3,4,5$, without repetition of digits.
$\therefore 100$ 's place digit must be a non-zero number which can be filled in 5 ways.
10 's place digits can be filled in 5 ways.
Unit's place digit can be filled in 4 ways.
$\therefore$ total number of ways the number can be formed $=5 \times 5 \times 4=100$
$\therefore 100$ numbers between 100 and 1000 can be formed.

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