Find the number of integers in the set {1,2,3,....,2009} whose sum of the digits is 11.
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Answer: 77
Step-by-step explanation:
Coefficient of x
10
in (x+x
2
+x
3
)
7
= coefficient of x
3
in (1+x+x
2
)
7
= coefficient of x
3
in (1−x
3
)
7
(1−x)
−7
=
7+3−1
C
3
−7
=
9
C
3
−7
=
6
9×8×7
−7=77
Alternate:
The digits are 1,1,1,1,1,2,3 or 1,1,1,1,2,2,2
Hence number of seven digit numbers formed =
5!
7!
+
4!3!
7!
=77
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