In how many ways can the team be formed?

Question

A middle school classroom contains 15 students. Out

of them, nine are boys. A team is to be formed with ten

students, of them six must be boys. In how many ways

can the team be formed?Explain?

Answer 1

This is a classic hypergeometric distribution question and you should be able to write the answer down directly as

₉C₆ * ₆C₄ / ₁₅C_{10 where the C's are the binomial coefficients.}

_{The first is the number of ways of picking 6 boys from the 9 available, the second is the number of ways of picking 4 other (presumably girls) from the other 6 students.}

_{The numerator is the answer to the problem. The denominator is the number of ways of picking 10 from a group of 15 and the quotient is the probability of picking 9 boys and 6 girls for the team.}

Answer 2

(₉C₆)(₆C₃) = ?