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Question
Mathematics
The coefficient of x7 in the expansion of (1-x-x2+x3)6 is
Q. The coefficient of
x
7
in the expansion of
(
1
−
x
−
x
2
+
x
3
)
6
is
1461
277
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A
132
B
144
C
-132
D
-144
Solution:
We have
(
1
−
x
−
x
2
+
x
3
)
6
=
(
1
−
x
)
6
(
1
−
x
2
)
6
coefficient of
x
7
in
(
1
−
x
−
x
2
+
x
3
)
6
=
6
C
1
⋅
6
C
3
−
6
C
3
⋅
6
C
2
+
6
C
5
⋅
6
C
1
=
6
×
20
−
20
×
15
+
6
×
6
=
−
144