(C) $5$-digit number cannot start with $0$. Total permutations of $5$ distinct digits taken all at once is $^5P_5 = 5! = 120$. Numbers starting with $

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(C) $5$-digit number cannot start with $0$. Total permutations of $5$ distinct digits taken all at once is $^5P_5 = 5! = 120$. Numbers starting with $0$ are formed by arranging the remaining $4$ digits in the last $4$ positions,which is $^4P_4 = 4! = 24$. Therefore,the number of $5$-digit numbers is $120 - 24 = 96$.

Class 11 Mathematics Permutations and Combinations Definition of permutation, Number of permutations with or without repetition, Conditional permutations

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Using the digits $0, 2, 4, 6, 8$ not more than once in any number,the number of $5$-digit numbers that can be formed is:

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A
$16$
B
$24$
C
$96$
D
$120$

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Permutations and Combinations

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

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Using the digits $0, 2, 4, 6, 8$ not more than once in any number,the number of $5$-digit numbers that can be formed is:

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