Question

The sum of the numbers which are greater than $1000$ formed by the digits $1,3,5,7,$ using each digit once.

Answer 1

we have,

number of digi$t=1,3,5,7$

Total formed of No$=4,3,2,1$

by using$\left(1.35.7\right)----$

$=4\times 3\times 2\times 1\times =24$

$6\times 1\times 1+6\times 1\times 10+6\times 1\times 100+6\times 1\times 1\times 1000$

$+6\times 3\times 1+6\times 30\times 10+6\times 3\times 100\times +6\times 3$

$\times 1000\times 6\times 5\times (76\times 5010+6\times$

$5\times 100+6\times 7\times 1+6\times 7\times 10+$

$6\times 7\times 100+6\times 7\times 1000$

$=(6\times +1+1+6\times 3\times 1+6\times 5\times 176\times 7\times 1)$

$+6\times 10(1+3+5+1)+6\times 100$

$(1+3+5+7)+60\times 1000(1+3+7)$

$=6\times (1+3+5+7)+6\times 100(1+3+5+7)$

$+6\times 100(1+3+5+7)+6\times 1000$

$(1+3+5+7)$

$=(1+3+5+7)+6[1+10\times 100+1000)$

$=16\times 6\times 1111$

$=106656$

Hence this is the answer