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Algebra
1 Feb 2012 13:59:55 IST
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all the numbers formed by using 5 or all 6 of the digits given are greater than 10,000.
so checking the number of itmes a digit occurs on a place.
eg:
making a five digit number with 1 as 1st digit...
1_ _ _ _ 5C4 * 4! = 120......i.e. 1 will occur on first place 120 times similarly all the numbers will occur on all the places 120 times..
so, the sum 6+5+4+3+2+1 = 21.
lets add it from first place to fifth place 120 times.
21*120 + 21*120*10(tenth place) + 21*120*100 (hundreth place) + 21*120*1000 + 21*120*10000.......eq1
now for 6 digit numbers..........
its the same way...
6 _ _ _ _ _
6 comes on the place 5! times as the places can be filled in 5! ways....
thrfr the sum will come on every place 5! times!!!
5! = 120
21 * 120 + 21*120*10 + 21*120*100 + 21*120*1000 + 21*120*10000 + 21*120*100000.........eq2
add both!!