Answer:
[tex]\dfrac{1}{35}[/tex]
Step-by-step explanation:
Given:
Total number of students in a class = 7
Number of students who play soccer = 4
Number of students who don't play soccer = 3
Now, number of ways of choosing 3 students out of 7 students is given by their combination.
So, number of ways of choosing 3 students (S)= [tex]_{3}^{7}\textrm{C}=\frac{7!}{3!\times 4!}=\frac{7\times 6\times\times 5\times 4!}{3\times 2\times 4!}=35[/tex]
Now, number of choosing 3 students who don't play soccer out of 3 students is given by their combination and is given as:
N = [tex]_{3}^{3}\textrm{C}=1[/tex]
Therefore, the probability that none of the three of them play soccer is given as:
[tex]P(None\ play\ soccer)=\frac{N}{S}\\\\P(None\ play\ soccer)=\frac{1}{35}[/tex]
Therefore, the the probability that none of the three of them play soccer is [tex]\frac{1}{35}[/tex]
