Permutations And Combinations Question 17

Question: How many numbers lying between 10 and 1000 can be formed from the digits 1, 2, 3, 4, 5, 6, 7, 8, 9 (repetition is allowed)

Options:

A) 1024

B) 810

C) 2346

D) None of these

Show Answer

Answer:

Correct Answer: B

Solution:

  • The total number between 10 and 1000 are 989 but we have to form the numbers by using numerals $ 1,\ 2,……..9,\ \ i.e. $ 0 is not occuring so the numbers containing any ?0? would be excluded i.e., Required number of ways $ =989- \begin{cases} & 20,\ 30,\ 40,…………….100=9 \\ & 101,\ 102,……………….200=19 \\ & 201,……………………300=19 \\ & ……………………………………… \\ & ……………………………………… \\ & 901,……………………..990=18 \\ \end{cases} $ $ =989-(9+18+19\times 8)=810 $ . Aliter: Between 10 and 1000, the numbers are of 2 digits and 3 digits. Since repetition is allowed, so each digit can be filled in 9 ways. Therefore number of 2 digit numbers $ =9\times 9=81 $ and number of 3 digit numbers $ 9\times 9\times 9=729 $ Hence total ways $ =81+729=810 $ .

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