The total number of numbers greater than 100 | vedclass

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Question

(D) Numbers greater than $100$ can be either $3$-digit or $4$-digit numbers.For a number to be divisible by $5$,the digit $5$ must be at the units pla

Vedclass · Accepted Answer

$12$

Vedclass · Answer

(D) Numbers greater than $100$ can be either $3$-digit or $4$-digit numbers.For a number to be divisible by $5$,the digit $5$ must be at the units place.Case $I$: $3$-digit numbers.The units place is fixed as $5$. The remaining $2$ places can be filled by the remaining $3$ digits $(3, 4, 6)$ in $P(3, 2) = 3 	imes 2 = 6$ ways.Case $II$: $4$-digit numbers.The units place is fixed as $5$. The remaining $3$ places can be filled by the remaining $3$ digits $(3, 4, 6)$ in $P(3, 3) = 3 	imes 2 	imes 1 = 6$ ways.Total number of required numbers $= 6 + 6 = 12$.

The total number of numbers greater than $100$ and divisible by $5$,that can be formed from the digits $3, 4, 5, 6$,if no digit is repeated is:

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