# Combinations problem

#### Venk

##### New member
So my teacher told us a story about how when she was younger they had a pool of 145 questions for their exam and from these they draw 3 questions for you and hopefully you have studied for them. The thing is one student showed up with having studied for only 6 of the questions. It turned out that he had studied for 3 out of the 3 questions he recieved. What is the chance of that happening and do i calculate this.

#### pka

##### Elite Member
So my teacher told us a story about how when she was younger they had a pool of 145 questions for their exam and from these they draw 3 questions for you and hopefully you have studied for them. The thing is one student showed up with having studied for only 6 of the questions. It turned out that he had studied for 3 out of the 3 questions he recieved. What is the chance of that happening and do i calculate this.
Suppose the student chose only six particular, for whatever reasons to study. The student then has $$\displaystyle \dbinom{6}{3}=20$$ ways to have studied all three of the questions which will be chosen for him/her.
Now you post what you think. We can help if we know what you understand about this.