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Question
Mathematics
The value of the expression 47C4+ displaystyle ∑5j = 1 52-jC3 is
Q. The value of the expression
47
C
4
+
j
=
1
∑
5
52
−
j
C
3
is
1764
210
IIT JEE
IIT JEE 1980
Permutations and Combinations
Report Error
A
47
C
5
12%
B
52
C
5
20%
C
52
C
4
56%
D
None of these
12%
Solution:
Here,
47
C
4
+
j
=
1
∑
5
52
−
j
C
3
=
47
C
4
+
51
C
3
+
50
C
3
+
49
C
3
+
48
C
3
+
47
C
3
=
(
47
C
4
+
47
C
3
)
+
48
C
3
+
49
C
3
+
50
C
3
+
51
C
3
[using
n
C
r
+
n
C
r
−
1
=
n
+
1
C
r
]
=
(
48
C
4
+
a
48
C
3
)
+
49
C
3
+
50
C
3
+
51
C
3
=
(
49
C
4
+
49
C
3
)
+
50
C
3
+
51
C
3
=
(
50
C
4
+
50
C
3
)
+
51
C
3
=
51
C
4
+
51
C
3
=
52
C
4