Question

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 ?

Answer 1

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

Answer 2

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.

Answer 3

i still don't understand

Answer 4

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.

Answer 5

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

Answer 6

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

Answer 7

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

Answer 8

"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 "

Answer 9

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

Answer 10

ok thanks