How many numbers are there between 100 and 10 | vedclass

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(B) Any number between $100$ and $1000$ is a $3$-digit number.Since the digits must be distinct,repetition of digits from the set ${0, 1, 2, 3, 4, 5,

Vedclass · Accepted Answer

$648$

Vedclass · Answer

(B) Any number between $100$ and $1000$ is a $3$-digit number.Since the digits must be distinct,repetition of digits from the set ${0, 1, 2, 3, 4, 5, 6, 7, 8, 9}$ is not allowed.For a $3$-digit number,the hundreds place cannot be $0$.$1$. The hundreds place can be filled in $9$ ways (digits $1$ to $9$).$2$. The tens place can be filled in $9$ ways (any of the $10$ digits except the one used in the hundreds place,including $0$).$3$. The units place can be filled in $8$ ways (any of the $10$ digits except the two already used).Total number of such $3$-digit numbers $= 9 	imes 9 	imes 8 = 648$.

How many numbers are there between $100$ and $1000$ in which all the digits are distinct?

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