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?

0.1071

Step-by-step explanation:

Given

Total number of students=8

Boys=2

Girls=6

When we are picking a group from population we use combinations to calculate sample space and for event

So if a group of 5 has to be picked from 8 students

ⁿC_k=  n!/(k!)(n-k)!

C_(n,k)=  n!/(k!)(n-k)!

Here n=8 and k=5

C_8,5=  8!/(5!)(8-5)!

This will give us:  

C_8,5=56

And if we have to pick only girls:

C_6,5=  6!/(5!)(6-5)!

=6

The probability of picking all girls:

=6/56

=0.1071

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