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NDA Math Permutations and Combinations

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Question : 30 of 65

Marks: +1, -0

What is

C(47,4)+C(51,3)+C(50,3)

+C(49,3)+C(48,3)+C(47,3)

C(47, 4)
C(52, 5)
C(52, 4)
C(47, 5)

Solution:

Concept:

C(n, r-1)+C(n, r)=C(n+1, r)

Calculation:

\Rightarrow C(47,4)+C(51,3)+C(50,3)+C(49,3)+C(48,3)+C(47,3)

=\{C(47,4)+C(47,3)\}+C(51,3)+C(50,3)+C(49,3)+C(48,3)

As we know that, C

(n, r-1)+C(n, r)=C(n+1, r)

\Rightarrow\{C(47,4)+C(47,3)\}+C(51,3)+C(50,3)+C(49,3)+C(48,3)

=\{C(48,4)+C(48,3)\}+C(51,3)+C(50,3)+C(49,3)

\Rightarrow\{C(48,4)+C(48,3)\}+C(51,3)+C(50,3)+C(49,3)

=\{C(49,4)+C(49,3)\}+C(51,3)+C(50,3)

\Rightarrow\{C(49,4)+C(49,3)\}+C(51,3)+C(50,3)

=\{C(50,4)+C(50,3)\}+C(51,3)

\Rightarrow\{C(50,4)+C(50,3)\}+C(51,3)

=\{C(51,4)+C(51,3)\}

=C(52,4)

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