How many numbers less than 1000 can be made f | vedclass

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Question

(A) Numbers less than $1000$ can be $1$-digit,$2$-digit,or $3$-digit numbers.$1$-digit numbers: We can choose any of the $6$ digits. Number of ways $=

Vedclass · Accepted Answer

$156$

Vedclass · Answer

(A) Numbers less than $1000$ can be $1$-digit,$2$-digit,or $3$-digit numbers.$1$-digit numbers: We can choose any of the $6$ digits. Number of ways $= ^6P_1 = 6$.$2$-digit numbers: We can choose $2$ digits out of $6$ where order matters. Number of ways $= ^6P_2 = 6 	imes 5 = 30$.$3$-digit numbers: We can choose $3$ digits out of $6$ where order matters. Number of ways $= ^6P_3 = 6 	imes 5 	imes 4 = 120$.Total numbers $= 6 + 30 + 120 = 156$.

How many numbers less than $1000$ can be made from the digits $1, 2, 3, 4, 5, 6$ (repetition is not allowed)?

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