The number of 5-digit numbers that are not di | vedclass

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Question

(C) The set of available odd digits is $\{1, 3, 5, 7, 9\}$.Total number of $5$-digit numbers formed using these $5$ distinct digits is $5! = 120$.$A$

Vedclass · Accepted Answer

$96$

Vedclass · Answer

(C) The set of available odd digits is $\{1, 3, 5, 7, 9\}$.Total number of $5$-digit numbers formed using these $5$ distinct digits is $5! = 120$.$A$ number is divisible by $5$ if its last digit is $5$.If the last digit is fixed as $5$,the remaining $4$ positions can be filled by the remaining $4$ digits in $4!$ ways.Number of $5$-digit numbers divisible by $5 = 4! = 24$.Therefore,the number of $5$-digit numbers not divisible by $5 = 5! - 4! = 120 - 24 = 96$.

The number of $5$-digit numbers that are not divisible by $5$ and consist of different odd digits is:

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