Question

The sum of all possible numbers consisting of three digits formed out of $1,2,3,4,5$ no digit being repeated in any number, is:

• A. $19980$
• B. $99900$
• C. $39960$
• D. $39900$

Answer 1

The correct option is A $19980$

Sum of number containing $r$ digits given $n$ digits is
$\left(\mathrm{11.......}rtimes\right)\times {(}^{n-1}{P}_{r-1})\times$ (sum of $n$ digits)
$=\left(111\right)\times {(}^{5-1}{P}_{3-1})\times (5+4+3+2+1)$
$=111\times 12\times 15$
$=19980$