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Byju's Answer
Standard XII
Mathematics
nCr Definitions and Properties
If ∑i=12020 C...
Question
If
20
∑
i
=
1
(
20
C
i
−
1
20
C
i
+
20
C
i
−
1
)
3
=
k
21
,
then
k
equals :
A
50
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B
100
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C
200
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D
400
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Solution
The correct option is
B
100
(
20
C
i
−
1
20
C
i
+
20
C
i
−
1
)
=
(
20
C
i
−
1
21
C
i
)
∵
n
C
r
+
n
C
r
−
1
=
n
+
1
C
r
⇒
(
20
!
(
i
−
1
)
!
⋅
(
20
−
i
+
1
)
)
⋅
(
i
!
(
21
−
i
)
!
21
!
)
=
i
21
∴
20
∑
i
=
1
(
20
C
i
−
1
20
C
i
+
20
C
i
−
1
)
3
=
20
∑
i
=
1
(
i
21
)
3
=
1
(
21
)
3
(
20
×
(
20
+
1
)
2
)
2
=
100
21
Hence,
k
=
100
Suggest Corrections
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