Question

The number of numbers that can be formed with the help of the digits $1,2,3,4,3,2,1$ so that odd digits always occupy odd places, is

• A. $24$
• B. $18$
• C. $12$
• D. $30$

Answer 1

The correct option is B

$18$

Explanation for the correct options:

Find the number of required numbers.

The digits $1,2,3,4,3,2,1$ are given.

Find the number of numbers that can be formed from the given digits so that odd digits always occupy odd places.

We have four odd numbers $1,3,3,1$ and four odd places.

So, the total number of arrangements of these four numbers are $\frac{4!}{2!2!}=6$.

Also, We have three odd numbers $2,4,2$ and three remaining places.

So, the total number of arrangements of these three numbers are $\frac{3!}{2!}=3$.

Thus, the total number of required arrangements are $6\times 3=18$.

Hence, option $B$ is the correct answer.