Question

If the Math Olympiad Club consists of 11 students, how many different teams of 3 students can be formed for competitions?

Answer 1

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:

$C=\frac{m!}{n!*(m-n)!}$

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:

• n: 3
• m: 11

Replacing:

$C=\frac{11!}{3!*(11-3)!}$

Solving:

$C=\frac{11!}{3!*8!}$

being:

• 3!=3*2*1=6
• 8!=8*7*6*5*4*3*2*1=40,320
• 11!=39,916,800

So:

$C=\frac{39,916,800}{6*40,320}$

C= 165

165 different teams of 3 students can be formed for competitions