Numbers greater than 1000 but not greater tha | vedclass

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Question

(B) The numbers are $4$-digit numbers formed using the set $\{0, 1, 2, 3, 4\}$.Since the number must be greater than $1000$ and less than or equal to

Vedclass · Accepted Answer

$375$

Vedclass · Answer

(B) The numbers are $4$-digit numbers formed using the set $\{0, 1, 2, 3, 4\}$.Since the number must be greater than $1000$ and less than or equal to $4000$,the first digit can be $1, 2, 3,$ or $4$.Case $1$: First digit is $1, 2,$ or $3$.For each of these $3$ choices,the remaining $3$ positions can each be filled in $5$ ways (digits $0, 1, 2, 3, 4$).Total numbers for these cases $= 3 	imes 5 	imes 5 	imes 5 = 375$.However,we must exclude the case where the number is $1000$ (since it must be greater than $1000$).So,$375 - 1 = 374$ numbers.Case $2$: First digit is $4$.The only number $\le 4000$ starting with $4$ is $4000$ itself.Adding this to our count: $374 + 1 = 375$.Thus,the total count is $375$.

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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