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8 years, 6 months ago
8 years, 6 months ago
31235
first we consider 0 also in first place of three digit no
total digit with no repetition is equal to 10*9*8=720 means if we write all, then we found that we have 72 (1,2,3,4,5,6,7,8,9,0)
and the sum of 0 to 9 is 45 then multiply it to 72 because we have 72 set 45*72=3240, in all three same format sum of these line is 3240 using carry
so total is 359640,
but in this 0 also included in first place so now two digits no with no repition 81
for this again we take first place 0 for these two digit no total no now 90, we got now 9 set of (0,1,2,3,4,5,6,7,8,9) so sum 4450
but in this 0 also include in first place of two igit no and these no are 1,2,3,4,5,6,7,8,9 an the sum of these are 45
so total sum of two digit no with no repetition in other word three digit no starting with 0 is 4450-45=4405
now three digit with no repetition= 359640-4405=31235
8 years, 6 months ago
There are 900 3-digit numbers
(999 minus the 99 integers from 1 to 99), so we use: sum=n/2(ist term+final term) 900/2*(999+100)
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