Q67 / 180 · KCET 2024 · Mathematics

The value of ${ }^{49} C_3+{ }^{48} C_3+{ }^{47} C_3+{ }^{46} C_3+{ }^{45} C_3+{ }^{45} C_4$ is

  • Correct answer
    A
    ${ }^{50} C_4$
  • B
    ${ }^{50} C_3$
  • C
    ${ }^{50} C_2$
  • D
    ${ }^{50} C_1$

Solution

$\because{ }^n C_r+{ }^n C_{r+1}={ }^{n+1} C_{r+1}$ Given, ${ }^{49} C_3+{ }^{48} C_3+{ }^{47} C_3+{ }^{46} C_3+{ }^{45} C_3+{ }^{45} C_4$ $={ }^{49} C_3+{ }^{48} C_3+{ }^{47} C_3+{ }^{46} C_3+{ }^{46} C_4$ $={ }^{49} C_3+{ }^{48} C_3+{ }^{47} C_3+{ }^{47} C_4$ $={ }^{49} C_3+{ }^{48} C_3+{ }^{48} C_4$ $={ }^{49} C_3+{ }^{49} C_4={ }^{50} C_4$

Hence, the correct answer is option: 'A'.

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