Prove that 10c2 + 2x10c2 +10c4 = 12c4
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11th
Maths
Permutations and Combinations
Combinations
The value of 10C1 + 10C2 + ...
MATHS
The value of
10
C
1
+
10
C
2
+
10
C
3
+...+
10
C
9
is
MEDIUM
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VIDEO EXPLANATION
ANSWER
Consider (1+x)
10
=
10
C
0
x
10
+
10
C
1
x
9
+
10
C
2
x
8
+.........+
10
C
9
x+
10
C
10
Now substitute x=1 both sides
(1+1)
10
=
10
C
0
+
10
C
1
+
10
C
2
+.........+
10
C
9
+
10
C
10
⇒2
10
=1+
10
C
1
+
10
C
2
+.........+
10
C
9
+1
∴
10
C
1
+
10
C
2
+
10
C
3
+......+
10
C
9
=2
10
−2
Note:
n
C
0
=1 and
n
C
n
=1
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