Permutation and CombinationHard
Question
The number of integers which lie between 1 and 106 and which have the sum of the digits equal to 12 is:
Options
A.8550
B.5382
C.6062
D.8055
Solution
Let number be x1 x2 x3 x4 x5 x6
But Here x1 + x2 + .... x6 = 12
so coefficient of x12 in expansion (1 + x + x2 + .... + x9)6
= (1 - x10)6 . (1 - x)-6
⇒ 17C12 - 6C1 . 7C2
= 6188 - 126 = 6062
But Here x1 + x2 + .... x6 = 12
so coefficient of x12 in expansion (1 + x + x2 + .... + x9)6
= (1 - x10)6 . (1 - x)-6
⇒ 17C12 - 6C1 . 7C2
= 6188 - 126 = 6062
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