How many 3-digit numbers can be formed using | vedclass

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Question

(B) $3$-digit number consists of three places: Hundreds,Tens,and Units.For the Hundreds place,the digit '$0$' cannot be used because a $3$-digit numbe

Vedclass · Accepted Answer

$100$

Vedclass · Answer

(B) $3$-digit number consists of three places: Hundreds,Tens,and Units.For the Hundreds place,the digit '$0$' cannot be used because a $3$-digit number cannot start with $0$. Thus,we can choose from ${1, 3, 5, 7}$,which gives $4$ options.For the Tens place,since repetition is allowed,all $5$ digits ${0, 1, 3, 5, 7}$ can be used,giving $5$ options.For the Units place,since repetition is allowed,all $5$ digits ${0, 1, 3, 5, 7}$ can be used,giving $5$ options.Therefore,the total number of $3$-digit numbers $= 4 	imes 5 	imes 5 = 100$.

How many $3$-digit numbers can be formed using $0, 1, 3, 5, 7$ when repetition is allowed?

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