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permutation and combination — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHSpermutation and combination1 Mark
MCQ
$^{20}C_1 + 3 ^{20}C_2 + 3 ^{20}C_3 + ^{20}C_4$ is equal to-
  • A
    $^{20}C_4$
  • B
    $2. ^{21}C_4$
  • C
    $2. ^{22}C_4$
  • ✓
    $^{23}C_4$
✓

Answer

Correct option: D.
$^{23}C_4$
d
$({\,^{20}}{{\rm{C}}_1} + 2{\,^{20}}{{\rm{C}}_2} + {\,^{20}}{{\rm{C}}_3}{\rm{)}} + {{\rm{(}}^{20}}{{\rm{C}}_2} + 2{\,^{20}}{{\rm{C}}_3} + {\,^{20}}{{\rm{C}}_4}{\rm{)}}$

$ \Rightarrow {\,^{22}}{C_3} + {\,^{22}}{C_4} = {\,^{23}}{C_4}$

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