How many numbers divisible by 5 and lying bet | vedclass

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Question

(C) To form a number between $3000$ and $4000$,the thousands place must be occupied by the digit $3$. This is $1$ way.For the number to be divisible b

Vedclass · Accepted Answer

$^4P_2$

Vedclass · Answer

(C) To form a number between $3000$ and $4000$,the thousands place must be occupied by the digit $3$. This is $1$ way.For the number to be divisible by $5$,the units place must be occupied by the digit $5$. This is $1$ way.The remaining two places (hundreds and tens) must be filled by the remaining digits from the set ${1, 2, 4, 6}$.There are $4$ remaining digits and $2$ places to fill.The number of ways to arrange these is given by $^4P_2 = 4 	imes 3 = 12$.Thus,the total number of such numbers is $12$,which corresponds to $^4P_2$.

How many numbers divisible by $5$ and lying between $3000$ and $4000$ can be formed from the digits $1, 2, 3, 4, 5, 6$ (repetition is not allowed)?

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