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?

Question

asked Jun 26, 2021 165k views

2 Answers

TooCooL · Answer 1 · 2021-06-30T16:56:52+0000

Answer:

(1)/(35)

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)=
$_(3)^(7)\textrm{C}=(7!)/(3!* 4!)=(7* 6** 5* 4!)/(3* 2* 4!)=35$

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:

$P(None\ play\ soccer)=(N)/(S)\\\\P(None\ play\ soccer)=(1)/(35)$

Therefore, the the probability that none of the three of them play soccer is
(1)/(35)