Question

The number of $3$ digit numbers having exactly one of their digits as $5$, repetition is not allowed is

• A. $200$
• B. $216$
• C. $243$
• D. $210$

Answer 1

The correct option is A $200$

Consider $3$ digit number as $ABC$
Case $1$:
$A=5$, thus $B$ and $C$ can take $9$ and $8$ digits respectively
$\therefore$ Total numbers $=1\times 9\times 8=72$

Case $2$ :
$B=5$ or $C=5$
$A$ can take only $8$ digits as $0$ can't come,
$C/B$ can take $8$ digits.
$\therefore$ Total numbers
$=2\times 8\times 8=128$

Hence, the total required $3$ digit numbers
$=72+128=200$