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NDA 2019
Exam
NDA
Year
2019
Subject
Mathematics
Chapter
Permutation and Combination

NDA 2019 · Mathematics · Permutation and Combination

What is C(47,4)+C(51,3)+C(50,3)+C(49,3)+C(48,3)+ C (47,3) equal to?

What is C(47,4)+C(51,3)+C(50,3)+C(49,3)+C(48,3)+\mathrm{C}(47,4)+\mathrm{C}(51,3)+\mathrm{C}(50,3)+\mathrm{C}(49,3)+\mathrm{C}(48,3)+ C (47,3)(47,3) equal to?

Options

  1. AC(47,4)\mathrm{C}(47,4)
  2. BC(52,5)\mathrm{C}(52,5)
  3. CC(52,4)\mathrm{C}(52,4)
  4. DC(47,5)\mathrm{C}(47,5)

Correct answer

C. C(52,4)\mathrm{C}(52,4)

Step-by-step solution

47C4+47C3+48C3+49C3+50C3+51C3∵nCr+nCr−1=n+1Cr∴ we get 48C4+48C3+49C3+50C3+51C3=49C4+49C3+50C3+51C3=50C4+50C3+51C3\begin{aligned} & { }^{47} C_4+{ }^{47} C_3+{ }^{48} C_3+{ }^{49} C_3+{ }^{50} C_3+{ }^{51} C_3 \\ & \because{ }^n C_r+{ }^n C_{r-1}={ }^{n+1} C_r \\ & \therefore \text{ we get } \\ & { }^{48} C_4+{ }^{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\end{aligned}=51C4+51C3=52C4\begin{aligned} & ={ }^{51} C_4+{ }^{51} C_3 \\ & ={ }^{52} C_4\end{aligned}$
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