(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

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(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 $9 \times {}^{9}P_{4}$.

Class 11 Mathematics Permutation and Combination Definition of permutation, Number of permutations with or without repetition, Conditional permutations

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

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A
$99999$
B
$9 \times {}^{9}P_{4}$
C
${}^{10}P_{5}$
D
${}^{9}P_{4}$

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Class 11

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Permutation and Combination

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Definition of permutation, Number of permutations with or without repetition, Conditional permutations

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

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