There are 30 boys and 40 girls in a class a committee is to be formed by selecting 5 students
at random from the class. Find the probability that committee formed has 2 boys
Answers
Given : 30 boys and 40 girls in a class a committee is to be formed by selecting 5 students at random from the class
To find : probability that committee formed has 2 boys
Solution:
There are 30 boys and 40 girls in a class
=> total = 30 + 40 = 70 Students
Number of ways selecting 5 Student = ⁷⁰C₅
Committee formed has 2 Boys => committee has 3 Girls
Number of Ways of Selection = ³⁰C₂ * ⁴⁰C₃
Probability = ³⁰C₂ * ⁴⁰C₃ / ⁷⁰C₅
= (30 * 29 ) * (40 * 39 * 38 ) *( 5 * 4 * 3 * 2 * 1) / (2 * 3 * 2 )(70 * 69 * 68 * 67 * 66)
= 0.355
probability that committee formed has 2 boys = 0.355
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