The number of 3-digit odd numbers that can be | vedclass

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(B) $3$-digit number has three places: hundreds,tens,and units.For the number to be odd,the unit place must be filled by an odd digit from the given s

Vedclass · Accepted Answer

$108$

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(B) $3$-digit number has three places: hundreds,tens,and units.For the number to be odd,the unit place must be filled by an odd digit from the given set ${1, 2, 3, 4, 5, 6}$. The odd digits available are ${1, 3, 5}$. Thus,the unit place can be filled in $3$ ways.Since repetition is allowed,the hundreds place can be filled by any of the $6$ digits ${1, 2, 3, 4, 5, 6}$,which gives $6$ ways.The tens place can also be filled by any of the $6$ digits ${1, 2, 3, 4, 5, 6}$,which gives $6$ ways.Using the fundamental principle of counting,the total number of such odd numbers $= 6 	imes 6 	imes 3 = 108$.

The number of $3$-digit odd numbers that can be formed by using the digits $1, 2, 3, 4, 5, 6$ when the repetition is allowed,is

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