There are 10 students in a class: 6 boys and 4 girls. If the teacher picks a group of 3 at random, what is the probability that everyone in the group is a boy?

Answer:[tex]\dfrac{1}{6}[/tex].Step-by-step explanation:It is given that, Total number of students = 10 Number of boys = 6 Number of girls = 4 Total number of ways to select 3 students from 10 students. [tex]^{10}C_3=\dfrac{10!}{3!(10-3)!}=\dfrac{10\times 9\times 8\times 7!}{3\times 2\times 1\times 7!}=120[/tex] Total number of ways to select 3 students from 6 boys. [tex]^{6}C_3=\dfrac{6!}{3!(6-3)!}=\dfrac{6\times 5\times 4\times 3!}{3\times 2\times 1\times 3!}=20[/tex] The probability that everyone in the group is a boy is [tex]P=\dfrac{\text{Total number of ways to select 3 students from 6 boys}}{\text{Total number of ways to select 3 students from 10 students}}[/tex] [tex]P=\dfrac{20}{120}[/tex] [tex]P=\dfrac{1}{6}[/tex] Therefore, the required probability is 1/6.