If the number of five-digit numbers with dist | vedclass

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Question

(A) five-digit number is represented as $\_ \;\_\;\_\;\underline{2}\;\_$.The $10^{	ext{th}}$ place is fixed as $2$.For the $10,000^{	ext{th}}$ place

Vedclass · Accepted Answer

$8$

Vedclass · Answer

(A) five-digit number is represented as $\_ \;\_\;\_\;\underline{2}\;\_$.The $10^{	ext{th}}$ place is fixed as $2$.For the $10,000^{	ext{th}}$ place,we cannot use $0$ or $2$,so there are $8$ choices $(1, 3, 4, 5, 6, 7, 8, 9)$.For the $1,000^{	ext{th}}$ place,we can use $0$ and any of the remaining $7$ digits,so there are $8$ choices.For the $100^{	ext{th}}$ place,there are $7$ choices remaining.For the units place,there are $6$ choices remaining.Total number of such five-digit numbers $= 8 	imes 8 	imes 7 	imes 6 = 2688$.Given that the number is $336k$,we have $336k = 2688$.Therefore,$k = \frac{2688}{336} = 8$.

If the number of five-digit numbers with distinct digits and $2$ at the $10^{\text{th}}$ place is $336k$,then $k$ is equal to

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