If all the six digit numbers x 1 x 2 x 3 x 4 x 5 x 6 with 0 < x 1 < x 2 < x 3 < x 4 < x…

If all the six digit numbers x1x2x3x4x5x6 with 0<x1<x2<x3<x4<x5<x6 are arranged in the increasing order, then the sum of the digits in the 72th  number is _______.

Solution

Taking case 1 fixing 1 & 2 at first two places,

1 2        

So, other number can be selected in C47=35 ways as number are from 1-9

Case 2 fixing 1 & 3 at first two place,

1 3        

So, other number can be selected inC46=15 ways

Similarly,

1 4        

So, other number can be selected inC45=5 ways

Now fixing 1 & 5 we get,

1 5        

Other number can be selected inC44=1

Now fixing 2 & 3 in first two place,

2 3        

So, other number can be selected in C46=15

So, the 72nd number will be 245678

Hence, sum will be 2+4+5+6+7+8=32

Asked in: JEE Main 2023 (29 Jan Shift 1)

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