The number of three-digit numbers in which 9 | vedclass

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Question

(D) three-digit number is of the form $abc$,where $a \in \{1, 2, \dots, 9\}$ and $b, c \in \{0, 1, \dots, 9\}$.Case $1$: $9$ is at the hundreds place

Vedclass · Accepted Answer

$225$

Vedclass · Answer

(D) three-digit number is of the form $abc$,where $a \in \{1, 2, \dots, 9\}$ and $b, c \in \{0, 1, \dots, 9\}$.Case $1$: $9$ is at the hundreds place $(a=9)$.Then $b \in \{0, 1, \dots, 8\}$ ($9$ choices) and $c \in \{0, 1, \dots, 8\}$ ($9$ choices).Number of such integers $= 1 	imes 9 	imes 9 = 81$.Case $2$: $9$ is at the tens place $(b=9)$.Then $a \in \{1, 2, \dots, 8\}$ ($8$ choices) and $c \in \{0, 1, \dots, 8\}$ ($9$ choices).Number of such integers $= 8 	imes 1 	imes 9 = 72$.Case $3$: $9$ is at the units place $(c=9)$.Then $a \in \{1, 2, \dots, 8\}$ ($8$ choices) and $b \in \{0, 1, \dots, 8\}$ ($9$ choices).Number of such integers $= 8 	imes 9 	imes 1 = 72$.Total number of such integers $= 81 + 72 + 72 = 225$.

The number of three-digit numbers in which $9$ appears in exactly one place is

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