How many numbers less than 1000 can be formed | vedclass

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Question

(B) Numbers less than $1000$ can be $1$-digit,$2$-digit,or $3$-digit numbers.Case $1$: $1$-digit numbers using ${0, 1, 2, 4, 5}$. The digit $0$ is usu

Vedclass · Accepted Answer

$68$

Vedclass · Answer

(B) Numbers less than $1000$ can be $1$-digit,$2$-digit,or $3$-digit numbers.Case $1$: $1$-digit numbers using ${0, 1, 2, 4, 5}$. The digit $0$ is usually not considered a $1$-digit number in this context,so we have $4$ choices $(1, 2, 4, 5)$.Case $2$: $2$-digit numbers. The first digit cannot be $0$ ($4$ choices: $1, 2, 4, 5$). The second digit can be any of the remaining $4$ digits (including $0$). Total = $4 	imes 4 = 16$.Case $3$: $3$-digit numbers. The first digit cannot be $0$ ($4$ choices). The second digit can be any of the remaining $4$ digits. The third digit can be any of the remaining $3$ digits. Total = $4 	imes 4 	imes 3 = 48$.Total numbers = $4 + 16 + 48 = 68$.

How many numbers less than $1000$ can be formed using the digits $0, 1, 2, 4,$ and $5$ if repetition of digits is not allowed?

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