Question

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 1

Answer:

$\dfrac{1}{6}$.

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.

$^{10}C_3=\dfrac{10!}{3!(10-3)!}=\dfrac{10\times 9\times 8\times 7!}{3\times 2\times 1\times 7!}=120$

Total number of ways to select 3 students from 6 boys.

$^{6}C_3=\dfrac{6!}{3!(6-3)!}=\dfrac{6\times 5\times 4\times 3!}{3\times 2\times 1\times 3!}=20$

The probability that everyone in the group is a boy is

$P=\dfrac{\text{Total number of ways to select 3 students from 6 boys}}{\text{Total number of ways to select 3 students from 10 students}}$

$P=\dfrac{20}{120}$

$P=\dfrac{1}{6}$

Therefore, the required probability is 1/6.