Question

select the correct answer from the drop-down menu.

drews school is forming a planning committee for an upcoming cultural festival. the committee of 4 members is to be selected from among 10 teachers and 6 students.

the probability that the committee contains exactly two members from each group is choose an answer.

options:
45/728
135/364
229/364
683/728

Explanation:

Calculate the total number of ways to choose the committee

$$ \binom{16}{4} = \frac{16 \times 15 \times 14 \times 13}{4 \times 3 \times 2 \times 1} = 1820 $$

Calculate the number of favorable outcomes

$$ \binom{10}{2} \times \binom{6}{2} = 45 \times 15 = 675 $$

Calculate the probability

$$ P = \frac{675}{1820} = \frac{135}{364} $$

Answer:

• 45/728
• 135/364 (Correct answer)
• 229/364
• 683/728