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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:
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:
Solving:
being:
- 3!=3*2*1=6
- 8!=8*7*6*5*4*3*2*1=40,320
- 11!=39,916,800
So:
C= 165
<u><em>165 different teams of 3 students can be formed for competitions</em></u>
Area of the triangle = 6x + 36
Perimeter of the rectangle = 3x + 10
<h3>How to Find the Area and Perimeter of a Triangle?</h3>Given the following parameters of a triangle as shown in the image attached below, its area and perimeter is calculated as shown below?
Area of the triangle = 1/2(base)(height) = 1/2(12)(x + 6)
Area of the triangle = 6(x + 6)
Area of the triangle = 6x + 36
The perimeter of the triangle = sum of all the three sides of the given triangle = (x - 7) + (2x + 5) + (12)
Perimeter= x - 7 + 2x + 5 + 12
Add like terms
Perimeter= x + 2x - 7 + 5 + 12
Perimeter= 3x + 10
Therefore, we have:
Area of the triangle = 6x + 36
Perimeter of the rectangle = 3x + 10
Learn more about the area and perimeter of a rectangle on:
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