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 $2$. Since the digits must be distinct

Vedclass · Accepted Answer

$8$

Vedclass · Answer

(A) five-digit number is represented as $\_ \;\_\;\_\;\underline{2}\;\_$.The $10^{	ext{th}}$ place is fixed as $2$. Since the digits must be distinct,we cannot use $2$ in any other position.$1$. The $10,000^{	ext{th}}$ place (first digit) cannot be $0$ or $2$. Thus,there are $8$ choices $(1, 3, 4, 5, 6, 7, 8, 9)$.$2$. The $1,000^{	ext{th}}$ place can be any of the remaining $8$ digits (including $0$,excluding the digit used in the first place and $2$).$3$. The $100^{	ext{th}}$ place can be any of the remaining $7$ digits.$4$. The unit's place can be any of the remaining $6$ digits.Total number of such five-digit numbers $= 8 	imes 8 	imes 7 	imes 6 = 2688$.Given that the total number is $336k$,we have $336k = 2688$.$k = \frac{2688}{336} = 8$.

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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