Question

The number of $3$ digit odd numbers, that can be formed by using the digits $1,2,3,4,5,6$ when the repetition is allowed, is

• A. $60$
• B. $108$
• C. $36$
• D. $30$

Answer 1

The correct option is B $108$

$1,2,3,4,5,6$

$1,3,5$ are odd $\Rightarrow 3$ in numbers

$\Rightarrow$ in 3 ways ones digits

can be filled

Remaining 2 digits can be filled with any

of the 6 numbers $\Rightarrow 6$ ways

$\therefore$ using multiplication rule

Number of ways $=3\times 6\times 6=108$