The number of natural numbers less than 1000 | vedclass

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Question

(B) Natural numbers less than $1000$ can be one-digit,two-digit,or three-digit numbers.$1$. Three-digit numbers:The hundreds place can be filled in $9

Vedclass · Accepted Answer

$738$

Vedclass · Answer

(B) Natural numbers less than $1000$ can be one-digit,two-digit,or three-digit numbers.$1$. Three-digit numbers:The hundreds place can be filled in $9$ ways (digits $1-9$).The tens place can be filled in $9$ ways (digits $0-9$,excluding the digit used in the hundreds place).The units place can be filled in $8$ ways (remaining digits).Total three-digit numbers $= 9 	imes 9 	imes 8 = 648$.$2$. Two-digit numbers:The tens place can be filled in $9$ ways (digits $1-9$).The units place can be filled in $9$ ways (digits $0-9$,excluding the digit used in the tens place).Total two-digit numbers $= 9 	imes 9 = 81$.$3$. One-digit numbers:There are $9$ one-digit numbers ($1$ to $9$).Total natural numbers $= 648 + 81 + 9 = 738$.

The number of natural numbers less than $1000$ in which no digit is repeated is

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