Question

The sum of all the numbers which can be formed by using the digits $1,3,5,7$ all at a time and which have no digit repeated, is?

• A. $16\times 4!$
• B. $1111\times 3!$
• C. $16\times 1111\times 3!$
• D. $16\times 1111\times 4!$

Answer 1

Answer: (C)

$16\times 1111\times 3!$

Sum of the numbers $\left(S\right)$ formed by taking all the given $n$ digits is-

$S=\left(\text{sum of all digits}\right)\times (n-1)!\times \left(\mathrm{111....}\text{n times}\right)$

Now according to the question, the digits are $1,3,5,7$

$\therefore n=4$

Sum of digits $=1+3+5+7=16$

$\therefore S=16\times 3!\times 1111$

Hence the correct answer is (C) $16\times 3!\times 1111$.