The number of all 5-digit numbers with distin | vedclass

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Question

(B) $5$-digit number cannot have $0$ at the first position (ten-thousands place). For the first position, we have $9$ choices (digits $1$ to $9$). For

Vedclass · Accepted Answer

$9 	imes {}^{9}P_{4}$

Vedclass · Answer

(B) $5$-digit number cannot have $0$ at the first position (ten-thousands place). For the first position, we have $9$ choices (digits $1$ to $9$). For the remaining $4$ positions, we need to choose $4$ digits from the remaining $9$ available digits (including $0$ and excluding the digit used in the first position). The number of ways to arrange these $4$ digits is ${}^{9}P_{4}$. Therefore, the total number of $5$-digit numbers with distinct digits is $9 	imes {}^{9}P_{4}$.

The number of all $5$-digit numbers with distinct digits is:

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