How many numbers greater than 100 and divisib | vedclass

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(B) Numbers divisible by $5$ must have the digit $5$ fixed in the units place.Case $1$: $3$-digit numbers.The units place is fixed with $5$. The remai

Vedclass · Accepted Answer

$12$

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(B) Numbers divisible by $5$ must have the digit $5$ fixed in the units place.Case $1$: $3$-digit numbers.The units place is fixed with $5$. The remaining $2$ places (hundreds and tens) can be filled by the remaining $3$ digits $(3, 4, 6)$ in $^3P_2$ ways.$^3P_2 = \frac{3!}{(3-2)!} = 3 	imes 2 = 6$ ways.Case $2$: $4$-digit numbers.The units place is fixed with $5$. The remaining $3$ places (thousands,hundreds,and tens) can be filled by the remaining $3$ digits $(3, 4, 6)$ in $^3P_3$ ways.$^3P_3 = \frac{3!}{(3-3)!} = 3 	imes 2 	imes 1 = 6$ ways.Total numbers $= 6 + 6 = 12$.

How many numbers greater than $100$ and divisible by $5$ can be made from the digits $3, 4, 5, 6$,if no digit is repeated?

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