Question

Teesha is in the French club. There are 26 students in the club. The French teacher will pick 3 students at random to guide visiting students from France. What is the probability that Teesha will not be picked as a guide?

Answer 1

`~=88.5%`

Explanation:

First let's figure out the number of combinations we have with 26 students and picking 3:

`C_(26,3)=(26!)/((3!)(23!))=(26xx25xxcancel24^4xxcancel23!)/((cancel6)cancel(23!))=26xx25xx4=2600`

The next question is now how many ways can Teesha be not chosen? To do that, we simply reduce the number of candidates by one and see how many combinations there are:

`C_(25,3)=(25!)/((3!)(22!))=(25xxcancel24^4xx23xxcancel22!)/((cancel6)cancel(22!))=25xx4xx23=2300`

So the probability that she won't be picked is:

`=2300/2600=23/26~=0.885~=88.5%`