Question

There are 22 students, from which 6 people will be selected to be on a panel. If Allen and joe are 2 of the 22 students, then what is the probability that neither will be selected to be on the panel?

Answer 1

Solution:

We are given that: there are 22 students, from which 6 people will be selected to be on a panel.

Allen and Joe are 2 of the 22 students.

We have to find the probability that neither will be selected to be on the panel .

That is:

P( Neither Allen , nor Joe on the panel) = ..........?

Thus selected 6 students should be from rest of students except Allen and Joe.

Thus we have : rest of the students = 22 - 2 = 20

Thus selected 6 students should be from these 20 remaining students.

Thus

P( neither will be selected to be on the panel)

We use combination formula :

Thus

and

Thus we get:

P( neither will be selected to be on the panel)

We used rule:

6! gets cancel

14! gets cancel

20! gets cancel

Thus

P( neither will be selected to be on the panel) = 0.5195