Question

how many numbers are there between 100 and 1000 in which all the digits are distinct

Answer 1

648 numbers

(A) 900

(B) 648

(C) 720

(D) 252

(E) 729

We know that numbers between 100 and 1000 will be 3 digit integers. Let the arrangement be ABC where A,B,C represent distinct digits. We have 9 options for A (as 0 can not start a 3 digit number), 9 options again for B and 8 for C, giving a total of 9*9*8 = 648 options. B is the correct answer.

Answer 2

648 numbers are there between 100 and 1000 in which all the digits are distinct.

• To take all distinct digits i.e. without repetition numbers between 100 and 1000 are calculated in this way:
• As there are only 3 digits, first digit can be filled in 9 ways as we can't start with 0, second digit can be filled in 9 ways again as we can choose 0 and third digit in 8 ways.