Q67 / 150 · MHT CET 2009 · Mathematics

From a group of 8 boys and 3 girls, a commitee of 5 members to be formed. Find the probability that 2 particular girls are included in the committe is

  • A
    $\frac{4}{11}$
  • Correct answer
    B
    $\frac{2}{11}$
  • C
    $\frac{6}{11}$
  • D
    $\frac{8}{11}$

Solution

Total $\quad$ number $\quad$ of $\quad$ ways $={ }^{8} \mathrm{C}_{2}{ }^{3} \mathrm{C}_{3}+{ }^{8} \mathrm{C}_{3}{ }^{3} \mathrm{C}_{2}+{ }^{8} \mathrm{C}_{4}{ }^{3} \mathrm{C}_{1}+{ }^{8} \mathrm{C}_{5}{ }^{3} \mathrm{C}_{0}$ $=28 \times 1+56 \times 3+70 \times 3+56 \times 1$ $=462$ Number of ways in which 2 particular girls are included ${ }^{9} C_{3}=84$ $\therefore$ Required probability $=\frac{84}{462}=\frac{2}{11}$

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

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