## mathmath333 one year ago A teacher has to choose the maximum different groups of three students from a total of six students. Of these groups, in how many groups there will be included a particular student ?

1. mathmath333

\large \color{black}{\begin{align} & \normalsize \text{A teacher has to choose the maximum different }\hspace{.33em}\\~\\ & \normalsize \text{groups of three students from a total of six students. Of }\hspace{.33em}\\~\\ & \normalsize \text{these groups, in how many groups there will be included a }\hspace{.33em}\\~\\ & \normalsize \text{particular student ? }\hspace{.33em}\\~\\ \end{align}}

2. kropot72

Having chosen the particular student, there are 5 students remaining from which to choose two students. Therefore there are 5C2 ways of choosing three students, with each choice including the particular student.

3. mathmath333

i still don't understand

4. zzr0ck3r

you have 6 students, one student is in every group of 3, so you might as well pick that student. Well now there are 5 left and we want all the possible ways of choosing 2 of them to join our original student to make a group of three, i.e. 5c2.

5. zzr0ck3r

this is why the power set of a set of N elements has 2^N elements.

6. mathmath333

in the question it is not asked to choose 2 students out of remaining 5

7. zzr0ck3r

you are correct, but these groups of 3 that we have out of 6 people, all have 1 person in common, so it reduces to that problem

8. zzr0ck3r

"you have 6 students, one student is in every group of 3, so you might as well pick that student. Well now there are 5 left "

9. zzr0ck3r

do the same thing with 4 people instead of 6 and play with it on paper and you will see the idea

10. mathmath333

ok thanks