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5 digit numbers are possible from digits 1, 2, 3, 4, 5, 6, 7  When each digit is distinct is  7P5 .  what is sum of all such numbers?

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7P5=2520.
Now, since 5 digit no. is made by all possible permutations of 7 numbers i.e., 1,2,3,4,5,6&7(without repetition), so, each digit place of 5 digit no. will contain equal no. of 1's, 2's, 3's, 4's, 5's, 6's & 7's in total no.of permutations i.e., 2520.
That means if we consider ones place, then 2520/7=360 times it is occupied by 1, another 360 times it is occupied by 2 and so on upto 7. Similarly, each digit place of 5 digit no. will follow the same case.
Hence, if we add them all, it will be like-
for ones - 1*(360*1+360*2+...+360*7)=360*28*1
for tens - 10*(360*1+360*2+...+360*7)=360*28*10
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for ten thousands - 10000*(360*1+360*2+...+360*7)=360*28*10000
Therefore the total sum will be- 360*28*(1+10+100+1000+10000)=360*28*11111=111998880
 

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