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(B) The numbers must be $4$-digit numbers since they are between $1000$ and $4000$.Let the $4$-digit number be represented as $d_1 d_2 d_3 d_4$.For th

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$375$

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(B) The numbers must be $4$-digit numbers since they are between $1000$ and $4000$.Let the $4$-digit number be represented as $d_1 d_2 d_3 d_4$.For the number to be greater than $1000$ and less than or equal to $4000$,the first digit $d_1$ can be $1, 2, 3,$ or $4$.Case $1$: If $d_1 = 1, 2,$ or $3$,then each of the remaining three positions $(d_2, d_3, d_4)$ can be filled by any of the $5$ digits $(0, 1, 2, 3, 4)$ in $5$ ways each.Number of such integers = $3 	imes 5 	imes 5 	imes 5 = 375$.However,this includes the number $1000$ (where $d_1=1, d_2=0, d_3=0, d_4=0$). Since the question asks for numbers strictly greater than $1000$,we must exclude $1000$.So,count = $375 - 1 = 374$.Case $2$: If $d_1 = 4$,the only number possible is $4000$ because any other combination like $4001$ would be greater than $4000$.Thus,we add $1$ for the number $4000$.Total numbers = $374 + 1 = 375$.

Numbers greater than $1000$ but not greater than $4000$ which can be formed with the digits $0, 1, 2, 3, 4$ (repetition of digits is allowed),are

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