# Circles

How many different circles is determined by 9 points at the plane, if 6 of them lie in a straight line?

Correct result:

n =  64

#### Solution:

$n_1 = C_{{ 3}}(9) = \dbinom{ 9}{ 3} = \dfrac{ 9! }{ 3!(9-3)!} = \dfrac{ 9 \cdot 8 \cdot 7 } { 3 \cdot 2 \cdot 1 } = 84 \ \\ n_2 = C_{{ 3}}(6) = \dbinom{ 6}{ 3} = \dfrac{ 6! }{ 3!(6-3)!} = \dfrac{ 6 \cdot 5 \cdot 4 } { 3 \cdot 2 \cdot 1 } = 20 \ \\ n = n_1 - n_2 = 84 - 20 = 64$

Our examples were largely sent or created by pupils and students themselves. Therefore, we would be pleased if you could send us any errors you found, spelling mistakes, or rephasing the example. Thank you!

Leave us a comment of this math problem and its solution (i.e. if it is still somewhat unclear...):

Be the first to comment!

Tips to related online calculators
Would you like to compute count of combinations?

#### You need to know the following knowledge to solve this word math problem:

We encourage you to watch this tutorial video on this math problem:

## Next similar math problems:

• Points in plane
The plane is given 12 points, 5 of which is located on a straight line. How many different lines could by draw from this points?
• Lines
In how many points will intersect 14 different lines, where no two are parallel?
• Trinity
How many different triads can be selected from the group 43 students?
• Fish tank
A fish tank at a pet store has 8 zebra fish. In how many different ways can George choose 2 zebra fish to buy?
• Hockey
Hockey match ended 8:2. How many different matches could be?
• Division
Division has 18 members: 10 girls and 6 boys, 2 leaders. How many different patrols can be created, if one patrol is 2 boys, 3 girls and 1 leader?
• Chords
How many 4-tones chords (chord = at the same time sounding different tones) is possible to play within 7 tones?
• First class
The shipment contains 40 items. 36 are first grade, 4 are defective. How many ways can select 5 items, so that it is no more than one defective?
• Combinations
How many elements can form six times more combinations fourth class than combination of the second class?
• A student
A student is to answer 8 out of 10 questions on the exam. a) find the number n of ways the student can choose 8 out of 10 questions b) find n if the student must answer the first three questions c) How many if he must answer at least 4 of the first 5 qu
• College 2
College student is moving into a dormitory. The student rent a truck for $19.95 plus$0.99 per mile. Before returning the truck the student fills the tank with gasoline, which cost $65.32. Total cost$144.67. Using a linear equation, explain the process t
• Combinations
From how many elements we can create 990 combinations 2nd class without repeating?
• Teams
How many ways can divide 16 players into two teams of 8 member?
• Calculation of CN
Calculate: ?
• Parametric equation
Find the parametric equation of a line with y-intercept (0,-4) and a slope of -2.
• Line
It is true that the lines that do not intersect are parallel?
• Cards
Suppose that are three cards in the hats. One is red on both sides, one of which is black on both sides, and a third one side red and the second black. We are pulled out of a hat randomly one card and we see that one side of it is red. What is the probab