Question

Total number of six-digit numbers in which only and all the five digits $1,3,5,7$ and $9$ appear, is

• A. $5^6$
• B. $\frac{1}{2}·6!$
• C. $6!$
• D. $\frac{5}{2}(6!)$

Answer 1

The correct option is D

$\frac{5}{2}(6!)$

Explanation for the correct option:

Find the required number of numbers.

In the question, five digits $1,3,5,7$ and $9$ are given.

Since we have to find the number of six-digits numbers that can be formed using all the given digits.

So, the $5$ digits can be selected in $5$ digits by $1$ way and the $6^{th}$ digit can be selected by ${}^{5}C_1=5$.

And the permutations of the six digits can be done by $\frac{6!}{2}$.

Therefore, the total number of six-digit numbers in which only and all the five digits $1,3,5,7$ and $9$ appear is $\frac{5}{2}(6!)$.

Hence, option $D$ is the correct answer.