We have to arrange 6 books.
The number of permutations of n objects is n! = n. (n ? 1) . (n ? 2) ... 2.1
Here n = 6 and therefore, number of permutations is 6.5.4.3.2.1 = 720
The number of arrangements of 4 different digits taken 4 at a time is given by = 4! = 24.All the four digits will occur equal number of times at each of the position,namely ones,tens,hundreds,thousands.
Thus,each digit will occur 24/4 = 6 times in each of the position.The sum of digits in one's position will be 6 x (1+3+5+7) = 96.Similar is the case in ten's,hundred's and thousand's places.
Therefore,the sum will be 96 + 96 x 10 + 96 x 100 + 96 x 100 = 106656
In a 3 digit number one?s place can be filled in 5 different ways with (0,2,4,6,8)
10?s place can be filled in 10 different ways
100?s place can be filled in 9 different ways
There fore total number of ways = 5X10X9 = 450
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