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JEE Main 202329 JanuaryMorning Shift
Exam
JEE Main
Year
2023
Date
29 January
Shift
Morning Shift
Subject
Mathematics
Chapter
Permutation and Combination

JEE Main 2023 · 29 January · Morning Shift · Mathematics · Permutation and Combination

If all the six digit numbers x _ 1 x _ 2 x _ 3 x _ 4 x _ 5 x _ 6...

If all the six digit numbers x1x2x3x4x5x6{x}_{1}{x}_{2}{x}_{3}{x}_{4}{x}_{5}{x}_{6} with 0<x1<x2<x3<x4<x5<x60 < {x}_{1} < {x}_{2} < {x}_{3} < {x}_{4} < {x}_{5} < {x}_{6} are arranged in the increasing order, then the sum of the digits in the 72th{72}^{\text{th}} number is _______.

Correct answer

0

Step-by-step solution

Taking case (1)\left(1\right) fixing 1 and  1 \text{\text{ and } } 2 at first two places,

11 22

So, other number can be selected in C47=35C4 7 = 35 ways \left\{\text{as number arefromfrom1-9}\right\}</p><p>Case(2)</p><p>Case \left(2\right) fixing 1 and  1 \text{\text{ and } } 3 at first two place,

11 33

So, other number can be selected inC46=15C4 6 = 15 ways

Similarly,

11 44

So, other number can be selected inC45=5C4 5 = 5 ways

Now fixing 1 and  1 \text{\text{ and } } 5 we get,

11 55

Other number can be selected inC44=1C4 4 = 1

Now fixing 2 and  2 \text{\text{ and } } 3 in first two place,

22 33

So, other number can be selected in C46=15C4 6 = 15

So, the 72nd{72}^{nd} number will be 245678245678

Hence, sum will be 2+4+5+6+7+8=322 + 4 + 5 + 6 + 7 + 8 = 32

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