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permutation and combination — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHSpermutation and combination1 Mark
MCQ
Out of $18$ points in a plane, no three are in the same straight line except five points which are collinear. The number of $(i)$ straight lines, $(ii)$ triangles which can be formed by joining them is
  • A
    $(i )\,140 \,(ii) \,816$
  • B
    $(i) \,142,\,(ii)\,800$
  • ✓
    $(i) \,144,\,(ii)\, 806$
  • D
    $(i) \,146,\,(ii)\,750$
✓

Answer

Correct option: C.
$(i) \,144,\,(ii)\, 806$
c
(c) $18$ points, $5 $ collinear :

$(i)$ Number of lines${ = ^{18}}{C_2}{ - ^5}{C_2} + 1 = 153 - 10 + 1 = 144$

$(ii)$ Number of $\Delta s{ = ^{18}}{C_3}{ - ^5}{C_3} = 816 - 10 = 806$

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