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STD 11 - 6. permutation and combination — JEE STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceJEESTD 11 - 6. permutation and combination4 Marks
MCQ
The value of ${}^{50}{C_4} + \sum\limits_{r = 1}^6 {^{56 - r}{C_3}} $ is
  • A
    $^{56}{C_3}$
  • ✓
    $^{56}{C_4}$
  • C
    $^{55}{C_4}$
  • D
    $^{55}{C_3}$
✓

Answer

Correct option: B.
$^{56}{C_4}$
b
(b) ${\,^{50}}{C_4} + \,\left( {^{50}{C_3}{ + ^{51}}{C_3} + {\,^{52}}{C_3} + ......{\,^{55}}{C_3}} \right)$.

Taking first two terms together and adding them and following the same pattern, we get${\,^{56}}{C_4}$, $[As\,{\,^n}{C_r} + {\,^n}{C_{r - 1}} = {\,^{n + 1}}{C_r}]$.

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