Question

The sum of all 4 digit numbers that can be formed with the digits 1, 2, 3, 4, 5, 6 is (repetition not allowed):

• A. $1260\times 1111$
• B. $1800\times 111$
• C. $1800\times 1111$
• D. $720\times 111$

Answer 1

The correct option is A $1260\times 1111$

For every four set of digits chosen,

we know that the sum of all 4 digit numbers $=6\times$ sum of the digits chosen$\times (1000+100+10+1)$

Number of $4$ digit sets that can be chosen from given $6$ digits ${=}^6{C}_4=15$

i.e every digit occurs 10 times in all the 15 sets formed

$\therefore$ The sum of all four digit numbers that can be formed $=6\times 10(1+2+3+4+5+6)\times (1000+100+10+1)$

$=1260\times 1111$