How many numbers lying between 100 and 1000 c | vedclass

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(A) Every number between $100$ and $1000$ is a $3$-digit number. To form a $3$-digit number,the hundreds place cannot be $0$. The hundreds place can b

Vedclass · Accepted Answer

$100$

Vedclass · Answer

(A) Every number between $100$ and $1000$ is a $3$-digit number. To form a $3$-digit number,the hundreds place cannot be $0$. The hundreds place can be filled by any of the $5$ digits $(1, 2, 3, 4, 5)$,so there are $5$ choices. The tens place can be filled by any of the remaining $5$ digits (including $0$),so there are $5$ choices. The units place can be filled by any of the remaining $4$ digits,so there are $4$ choices. Therefore,the total number of such $3$-digit numbers is $5 	imes 5 	imes 4 = 100$.

How many numbers lying between $100$ and $1000$ can be formed with the digits $0, 1, 2, 3, 4, 5$,if the repetition of the digits is not allowed?

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