Answer:
165 different teams of 3 students can be formed for competitions
Step-by-step explanation:
Combinations of m elements taken from n in n (m≥n) are called all possible groupings that can be made with the m elements so that:
- Not all items fit
- No matter the order
- Elements are not repeated
That is, a combination is an arrangement of elements where the place or position they occupy within the arrangement does not matter. In a combination it is interesting to form groups and their content.
To calculate the number of combinations, the following expression is applied:
[tex]C=\frac{m!}{n!*(m-n)!}[/tex]
It indicates the combinations of m objects taken from among n objects, where the term "n!" is called "factorial of n" and is the multiplication of all the numbers that go from "n" to 1.
In this case:
Replacing:
[tex]C=\frac{11!}{3!*(11-3)!}[/tex]
Solving:
[tex]C=\frac{11!}{3!*8!}[/tex]
being:
- 3!=3*2*1=6
- 8!=8*7*6*5*4*3*2*1=40,320
- 11!=39,916,800
So:
[tex]C=\frac{39,916,800}{6*40,320}[/tex]
C= 165
165 different teams of 3 students can be formed for competitions
