How many 4-digit numbers can be formed using | vedclass

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Question

(A) Total $4$-digit numbers that can be formed using the digits ${0, 1, 2, 3, 4, 5, 6, 7}$ (where the first digit cannot be $0$) is $7 	imes 8 	imes

Vedclass · Accepted Answer

$1522$

Vedclass · Answer

(A) Total $4$-digit numbers that can be formed using the digits ${0, 1, 2, 3, 4, 5, 6, 7}$ (where the first digit cannot be $0$) is $7 	imes 8 	imes 8 	imes 8 = 3584$.Total $4$-digit numbers that can be formed without using the digit $1$ (using digits ${0, 2, 3, 4, 5, 6, 7}$) is $6 	imes 7 	imes 7 	imes 7 = 2058$.The number of $4$-digit numbers containing at least one $1$ is the total number of $4$-digit numbers minus the number of $4$-digit numbers without any $1$.Required numbers $= 3584 - 2058 = 1526$.Note: The provided option $D$ $(750)$ is incorrect based on the standard interpretation of this combinatorial problem. The correct calculation yields $1526$.

How many $4$-digit numbers can be formed using the digits $0, 1, 2, 3, 4, 5, 6, 7$ such that at least one digit is $1$?

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