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

Answer:

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

Step-by-step 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:

$P^{n}_{k}=\frac{n!}{(n-k)!}$

where = n = number of elements  = n

k = number of elements choose = 2

$P^{n}_{2}=\frac{n!}{(n-2)!}=\frac{n\times (n-1)\times (n-2)!}{(n-2)!}$

$=n\times (n-1)$