Question

There are 6 sections in a school and the top 2 students from each section form the este club. A three
member team is to be formed from the elite club, such that no two student from the same sections
part of the team. The number of ways in which this team can be formed is
1. 120
2. 160
3. 240
4. 480​

Answer 1

Concept

If $n$ number of things are given, then number of ways to choose $r$ things is $nC_r$

Given

Number of sections$=6$, Number of students$=2$. Three students are to be chosen to form the elite club.

To find

Number of ways to form the elite team

Solution

Let

$A_1,A_2=$ Two top students chosen from first section

$B_1,B_2=$ Two top students chosen from second section etc.

Students chosen from $6$ sections are

$A_1A_2,B_1B_2,C_1C_2,D_1D_2,E_1E_2,F_1F_2$

Now first student can be chosen in $6C_1$ ways

Second student can be chosen in $5C_1$ ways

And Third student can be chosen in $4C_1$ ways

Total number of ways to form the elite club team is

$=6C_1\times 5C_1\times 4C_1\\=6\times 5\times 4\\=120$

As a result elite club team can be formed in $120$ ways