Question

In a class of 777, there are 444 students who play soccer. If the teacher chooses 333 students, what is the probability that none of the three of them play soccer?

Answer 1

Answer:

$\dfrac{1}{35}$

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)= $_{3}^{7}\textrm{C}=\frac{7!}{3!\times 4!}=\frac{7\times 6\times\times 5\times 4!}{3\times 2\times 4!}=35$

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 =  $_{3}^{3}\textrm{C}=1$

Therefore, the probability that none of the three of them play soccer is given as:

$P(None\ play\ soccer)=\frac{N}{S}\\\\P(None\ play\ soccer)=\frac{1}{35}$

Therefore, the the probability that none of the three of them play soccer is $\frac{1}{35}$