There are 8 students in a class: 2 boys and 6 girls. If the teacher picks a group of 5 at random, what is the probability that everyone in the group is a girl?

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Answer 1 · 2018-06-27T03:36:13

#6/56=3/28~~0.1071#

When picking 5 people from a group of 8, this is a combinations question:

#C_(n,k)=((n),(k))=(n!)/((k!)(n-k)!)# with #n="population", k="picks"#

And our question has:

#((8),(5))=56#

When looking at only having girls picked, there are:

#((6),(5))=6# ways that can happen.

Therefore the probability that all girls will be picked is:

#6/56=3/28~~0.1071#