How many numbers between 5000 and 10,000 can | vedclass

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(A) number between $5000$ and $10,000$ must be a $4$-digit number.The thousand's place can be filled by any of the digits ${5, 6, 7, 8, 9}$,which give

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$5 	imes ^8P_3$

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(A) number between $5000$ and $10,000$ must be a $4$-digit number.The thousand's place can be filled by any of the digits ${5, 6, 7, 8, 9}$,which gives $5$ possible ways.Since each digit can appear at most once,we have $8$ remaining digits to fill the remaining $3$ places.The number of ways to arrange $3$ digits out of $8$ is given by the permutation formula $^nP_r = \frac{n!}{(n-r)!}$.Thus,the number of ways to fill the remaining $3$ places is $^8P_3$.By the fundamental principle of counting,the total number of such numbers is $5 	imes ^8P_3$.

How many numbers between $5000$ and $10,000$ can be formed using the digits $1, 2, 3, 4, 5, 6, 7, 8, 9$ if each digit appears not more than once in each number?

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