How many numbers between 3000 and 4000 can be | vedclass

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Question

(A) For a number to be between $3000$ and $4000$,the thousands place must be $3$.For a number to be divisible by $5$,the units place must be $0$ or $5

Vedclass · Accepted Answer

$12$

Vedclass · Answer

(A) For a number to be between $3000$ and $4000$,the thousands place must be $3$.For a number to be divisible by $5$,the units place must be $0$ or $5$. Since $0$ is not in the given set,the units place must be $5$.Thus,the thousands place is fixed as $3$ and the units place is fixed as $5$.The remaining two places (hundreds and tens) must be filled using the remaining $4$ digits $(4, 6, 7, 8)$ without repetition.The number of ways to fill these $2$ places is given by the permutation formula $^4P_2$.$^4P_2 = \frac{4!}{(4-2)!} = 4 	imes 3 = 12$.Therefore,there are $12$ such numbers.

How many numbers between $3000$ and $4000$ can be formed using the digits $3, 4, 5, 6, 7, 8$ without repetition,such that the numbers are divisible by $5$?

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