How many numbers lying between 99 and 1000 ca | vedclass

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(A) The numbers lying between $99$ and $1000$ are all $3$-digit numbers.We have $6$ digits available: ${0, 2, 3, 6, 7, 8}$.$A$ $3$-digit number cannot

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$100$

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(A) The numbers lying between $99$ and $1000$ are all $3$-digit numbers.We have $6$ digits available: ${0, 2, 3, 6, 7, 8}$.$A$ $3$-digit number cannot have $0$ at the hundreds place.Total ways to arrange $3$ digits out of $6$ is given by $^6P_3 = 6 	imes 5 	imes 4 = 120$.However,we must exclude the cases where $0$ is at the hundreds place. If $0$ is fixed at the hundreds place,we need to arrange $2$ more digits from the remaining $5$ digits in the tens and units places. This is given by $^5P_2 = 5 	imes 4 = 20$.Therefore,the total number of valid $3$-digit numbers is $120 - 20 = 100$.

How many numbers lying between $99$ and $1000$ can be formed using the digits $2, 3, 7, 0, 8, 6$,if each digit can be used only once in each number?

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