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Grade: 11

find the sum of all 4-digit numbers that can be forned using the digits 1,3,5,7,9...explain in detail...

9 years ago

Answers : (1)

Sudheesh Singanamalla
114 Points

there are 5P4 ways of forming a 4 digit number with each digit appearing at most once.Consider first the one's place. In those 120 numbers, 1,3,5,7, and 9 appear exactly the same number of times, that is, each digit appears 120/5 = 24 times.

For the tens place, same thing: 1,3,5,7,and 9 appear equally the same number of times. Each digit appears 24 times.

The argument for the hundreds and thousands places are the same.

Thus the sum of all those distinct 120 numbers is
1,000*24*(1+3+5+7+9)+ 100*24*(1+3+5+7+9) + 10*24*(1+3+5+7+9) + 1*24*(1+3+5+7+9)

= 1,111*24*(1+3+5+7+9)

= 1,111*24*25

= 6,66,600


Please approve !

9 years ago
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