There are 10 students in a class: 6 boys and 4 girls. If the teacher picks a group of 4 at random, what is the probability that everyone in the group is a boy?

Probability that nbr1 is a boy is p1 = 6/10.

Probability that nbr2 is a boy, given 5 boys left is 5/9

Probability that nbr3 is a boy given 4 boys left is 4/8

Probability that nbr 4 is a boy given 3 boys left is 3/7

$${\mathtt{Overallprobability}} = {\frac{{\mathtt{6}}{\mathtt{\,\times\,}}{\mathtt{5}}{\mathtt{\,\times\,}}{\mathtt{4}}{\mathtt{\,\times\,}}{\mathtt{3}}}{\left({\mathtt{10}}{\mathtt{\,\times\,}}{\mathtt{9}}{\mathtt{\,\times\,}}{\mathtt{8}}{\mathtt{\,\times\,}}{\mathtt{7}}\right)}} \Rightarrow {\mathtt{Overallprobability}} = {\mathtt{0.071\: \!428\: \!571\: \!428\: \!571\: \!4}}$$

Approximately 0.071 or 7.1% 

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