How many numbers can be formed using the digi | vedclass

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Question

(B) To form a number between $3000$ and $4000$,the thousands place must be fixed as $3$.For the number to be divisible by $5$,the units place must be

Vedclass · Accepted Answer

$12$

Vedclass · Answer

(B) To form a number between $3000$ and $4000$,the thousands place must be fixed as $3$.For the number to be divisible by $5$,the units place must be $5$.We have used $2$ digits ($3$ and $5$) out of the given $6$ digits $(3, 4, 5, 6, 7, 8)$.The remaining digits are $4, 6, 7, 8$,which are $4$ in total.We need to fill the remaining two positions (hundreds and tens) using these $4$ digits without repetition.The number of ways to do this is given by the permutation formula $^nP_r = \frac{n!}{(n-r)!}$.Here,$n = 4$ and $r = 2$,so $^4P_2 = \frac{4!}{(4-2)!} = \frac{4 	imes 3 	imes 2!}{2!} = 12$.Thus,there are $12$ such numbers.

How many numbers can be formed using the digits $3, 4, 5, 6, 7, 8$ that lie between $3000$ and $4000$ and are divisible by $5$,given that repetition of digits is not allowed?

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