How many numbers lying between 10 and 1000 ca | vedclass

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(B) Between $10$ and $1000$,the numbers can be either $2$-digit numbers or $3$-digit numbers.Case $1$: $2$-digit numbers.Each of the $2$ places can be

Vedclass · Accepted Answer

$810$

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(B) Between $10$ and $1000$,the numbers can be either $2$-digit numbers or $3$-digit numbers.Case $1$: $2$-digit numbers.Each of the $2$ places can be filled by any of the $9$ digits ($1$ through $9$) because repetition is allowed.Number of ways $= 9 	imes 9 = 81$.Case $2$: $3$-digit numbers.Each of the $3$ places can be filled by any of the $9$ digits ($1$ through $9$) because repetition is allowed.Number of ways $= 9 	imes 9 	imes 9 = 729$.Total numbers $= 81 + 729 = 810$.

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)?

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