Permutations & Combinations
Committees
MMTS_Full_Test_16
Grade 12
Question:
A committee of 5 is to be chosen from a group of 9 people. The probability that a certain married couple will either serve together or not at all is
$\dfrac{1}{2}$
$\dfrac{5}{9}$
$\dfrac{4}{9}$
$\dfrac{2}{3}$
Step-by-Step Solution
Key Concept: Probability = (both in or both out) / total
Both in: $\binom{7}{3}=35$. Both out: $\binom{7}{5}=21$. Total: $\binom{9}{5}=126$. $P=(35+21)/126=56/126=4/9$.
Correct Answer: 1