MHT CET · Maths · Probability
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 \(\frac{4}{11}\)
- B \(\frac{2}{11}\)
- C \(\frac{6}{11}\)
- D \(\frac{8}{11}\)
Answer & Solution
Correct Answer
(B) \(\frac{2}{11}\)
Step-by-step Solution
Detailed explanation
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 \(=\frac{84}{462}=\frac{2}{11}\)
\(=28 \times 1+56 \times 3+70 \times 3+56 \times 1\)
\(=462\)
Number of ways in which 2 particular girls are included \({ }^{9} C_{3}=84\)
\(\therefore\) Required probability \(=\frac{84}{462}=\frac{2}{11}\)
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