Find the total number of seven digit numbers x1x2x3x4x5x6x7 having the property that x1 x2 < x3 < x4 x5 < x6 < x7.
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There are 9000000 seven digit numbers exist.
(because
smallest 7 digit number is 1000000 greatest 7 digit number is 9999999
So total number of 7 digit numbers=9999999 - 1000000+1).
Out of 9000000 numbers 4500000 are having the sum of digits as even and the remaining 4500000 are having the sum of digits as odd.
SinceEvery alternate number has its sum of digits even and odd.
For e.g. Sum of digits in 11 is 2 which is even. Sum of digits of 12 is 3 which is odd. Again sum of digits of 13 is even and that of 14 is odd. There are 9000000 seven digit numbers. So half of it is 4500000
So the required answer is 4500000.
(because
smallest 7 digit number is 1000000 greatest 7 digit number is 9999999
So total number of 7 digit numbers=9999999 - 1000000+1).
Out of 9000000 numbers 4500000 are having the sum of digits as even and the remaining 4500000 are having the sum of digits as odd.
SinceEvery alternate number has its sum of digits even and odd.
For e.g. Sum of digits in 11 is 2 which is even. Sum of digits of 12 is 3 which is odd. Again sum of digits of 13 is even and that of 14 is odd. There are 9000000 seven digit numbers. So half of it is 4500000
So the required answer is 4500000.
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