Question

The class has n students, and n is an even number. The students are forming teams to work on their homework. Each team has exactly 2 students and each student has to appear in exactly one team. How many distinct ways are there to form the teams for the class?

Answer 1

Distinct ways in which they all can form the teams for the class = n(n-1)

Explanation:

Total numbers of students = n (even number)

Number of student in each team = 2

Number of distinct ways are there to form the teams for the class:

`P^(n)_(k)=(n!)/((n-k)!)`

where = n = number of elements = n

k = number of elements choose = 2

`P^(n)_(2)=(n!)/((n-2)!)=(n* (n-1)* (n-2)!)/((n-2)!)`

`=n* (n-1)`