Question

four girls and six boys are in a spanish club. three of the people will be chosen at random to represent the group in a photograph.

what is the probability that one girl and two boys will be chosen?

Explanation:

Calculate the total number of ways to choose three people

$$ \binom{10}{3} = \frac{10 \times 9 \times 8}{3 \times 2 \times 1} = 120 $$

Calculate the number of favorable outcomes

$$ \binom{4}{1} \times \binom{6}{2} = 4 \times \frac{6 \times 5}{2 \times 1} = 4 \times 15 = 60 $$

Calculate the probability

$$ P = \frac{60}{120} = 0.5 = 50\% $$

Answer:

• 40%
• 50% (Correct answer)
• 70%
• 60%