How many 3-digit numbers,each less than 600,c | vedclass

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(A) $3$-digit number has three places: hundreds,tens,and units.Since repetition of digits is allowed,each place can be filled by any of the given digi

Vedclass · Accepted Answer

$180$

Vedclass · Answer

(A) $3$-digit number has three places: hundreds,tens,and units.Since repetition of digits is allowed,each place can be filled by any of the given digits $1, 2, 3, 4, 5, 9$ (total $6$ digits).For the hundreds place,the digit must be less than $6$ to ensure the number is less than $600$. Thus,the hundreds place can be filled by $1, 2, 3, 4,$ or $5$. This gives $5$ possible ways.The tens place can be filled by any of the $6$ digits $(1, 2, 3, 4, 5, 9)$ in $6$ ways.The units place can be filled by any of the $6$ digits $(1, 2, 3, 4, 5, 9)$ in $6$ ways.Therefore,the total number of such $3$-digit numbers $= 5 	imes 6 	imes 6 = 180$.

How many $3$-digit numbers,each less than $600$,can be formed from the digits $1, 2, 3, 4, 5,$ and $9$,if repetition of digits is allowed?

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