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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?

 Jun 4, 2021
 #1
avatar+2193 
+2

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. 

 

=^._.^=

 Jun 4, 2021
 #2
avatar+26213 
+4

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 \(\approx 28.57 \%\)

 

laugh

 Jun 4, 2021

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