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

CBSE BoardEnglish MediumSTD 11 ScienceMathsSTD 11 - 6. permutation and combination1 Mark
MCQ
$^n{C_r} + {2^n}{C_{r - 1}}{ + ^n}{C_{r - 2}} = $
  • A
    $^{n + 1}{C_r}$
  • B
    $^{n + 1}{C_{r + 1}}$
  • ✓
    $^{n + 2}{C_r}$
  • D
    $^{n + 2}{C_{r + 1}}$
✓

Answer

Correct option: C.
$^{n + 2}{C_r}$
c
(c) $^n{C_r} + 2{^n}{C_{r - 1}} + {\,^n}{C_{r - 2}} = {\,^n}{C_r} + {\,^n}{C_{r - 1}} + {\,^n}{C_{r - 1}} + {\,^n}{C_{r - 2}}$
$ = {\,^{n + 1}}{C_r} + {\,^{n + 1}}{C_{r - 1}} = {\,^{n + 2}}{C_r}$.

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