+8 There are 7 students in a class: 2 boys and 5 girls. If the teacher picks a group of 3 at random, what is the probability that everyone in the group is a girl?
+2407 5/7 * 4/6 * 3/5.
At first person she picks has 5/7 chance of being a girl, then 4/6, then 3/5.
=^._.^=
+26388 There are 7 students in a class: 2 boys and 5 girls.
If the teacher picks a group of 3 at random,
what is the probability that everyone in the group is a girl?
\(\begin{array}{|rcll|} \hline \dfrac{ \binom{2}{0}_{\text{Boys}}\binom{5}{3}_{\text{Girls} } } {\binom{7}{3}_{\text{Boys and Girls} } } &=& \dfrac{2}{7}\\ \text{or} \\ \dfrac{5}{7}*\dfrac{4}{6}*\dfrac{3}{5}&=& \dfrac{2}{7}\\ \hline \end{array}\)
The probability is \(\approx 28.57 \%\)
