How many 3-digit numbers are there with no di | vedclass

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(B) $3$-digit number consists of a hundreds place,a tens place,and a units place.For the hundreds place,the digit $0$ cannot be used,so there are $9$

Vedclass · Accepted Answer

$648$

Vedclass · Answer

(B) $3$-digit number consists of a hundreds place,a tens place,and a units place.For the hundreds place,the digit $0$ cannot be used,so there are $9$ possible choices $(1, 2, 3, 4, 5, 6, 7, 8, 9)$.For the tens place,any digit from $0$ to $9$ can be used except the one already placed in the hundreds place. Thus,there are $10 - 1 = 9$ choices.For the units place,any digit from $0$ to $9$ can be used except the two digits already placed in the hundreds and tens places. Thus,there are $10 - 2 = 8$ choices.Total number of $3$-digit numbers with no repeated digits $= 9 	imes 9 	imes 8 = 648$.

How many $3$-digit numbers are there with no digit repeated?

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