How many 3-digit odd numbers can be formed us | vedclass

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Question

(A) To form a $3$-digit odd number,the units place must be filled by an odd digit.The available odd digits from the set $\{1, 2, 3, 4, 5, 6, 7, 8, 9\}

Vedclass · Accepted Answer

$280$

Vedclass · Answer

(A) To form a $3$-digit odd number,the units place must be filled by an odd digit.The available odd digits from the set $\{1, 2, 3, 4, 5, 6, 7, 8, 9\}$ are $\{1, 3, 5, 7, 9\}$.There are $5$ choices for the units place.Since repetition is not allowed,after filling the units place,we have $8$ remaining digits to fill the tens place and $7$ remaining digits to fill the hundreds place.The number of ways to fill the tens place is $8$ and the number of ways to fill the hundreds place is $7$.Total number of $3$-digit odd numbers = $7 	imes 8 	imes 5 = 280$.

How many $3$-digit odd numbers can be formed using the digits $1, 2, 3, 4, 5, 6, 7, 8, 9$ if repetition of digits is not allowed?

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