What will be the value of sum of doublets formed by taking 2 integers from 1 to 10 at a time.

Question

Let S be the set of all 5 digit numbers formed by the digits 1, 2, 3, 4, 5 without repetition.
What is the sum of all numbers in S?

Answer 1

(1+2+3+ . . . . +10)2 = 12+22+32+ . . ....+102 + 2(sum of doublets)
Or 3025 = 385 + 2 (Sum of doublets)
Or Sum of doublets = (3025 - 385) / 2 = 1320

2nd
Sum = 1*( 2+3+....10) + 2* ( 3+4+5+..+10) + 3 * ( 4+5+...+10)+4( 5+6+..+10) +5* (6+7+..+10) +6(7+8+(+10) +7( 8+9+10) +8*(9+10) +9*10
= 54+ 2*52+3*49+4*45+5*40+6*34+7*27+8*19+ 90
= 1320