Out of 5 girls and 3 boys, 4 children are to be randomly selected for a quiz contest. What is the probability that all selected are girls?
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → \(\frac{1}{14}\)
Every group of 4 children out of the 8 is equally likely, so the probability is the number of all-girl groups divided by the number of all possible groups.
All possible groups: \({}^{8}C_4=\displaystyle\frac{8\times7\times6\times5}{4\times3\times2\times1}=70\)
Groups of 4 girls out of 5: \({}^{5}C_4=5\)
Probability \(=\displaystyle\frac{5}{70}=\frac{1}{14}\)