The first 5 odd natural numbers are written in every possible order. How many numbers can be formed if no repetition is allowed and what is their sum?

1) 5P5, 6666600
2) 5C1, 10^5
3) 51, 55555
4) 50, 666660
5) None of these

• The first five odd numbers are 1,3,5,7,9. Thus we have 5 numbers in total and no repetition is allowed while arranging.
  Any of the 5 numbers can be the ones position. Since a number has already occupied ones position, only the remaining 4 can fill up the tens position. If we consider this way, the no. of possible arrangements will be 1*2*3*4*5 which is nothing but 5!.. To find the sum, 5! is 120 and there are 5 numbers. each number would occur in the ones position 120/5 (i.e.24)times.
  
  Thus 1*24 + 3*24 +5*24 + 7*24 = 660.
  
  The correct answer is 5!numbers and sum is 6666600
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