Combinations

Take a set S of m different elements. Choose, in S, a subset of n elements. Such a choice is called a combination of m elements choose n. Two combinations are different if they have different elements. The number of these combinations is:

The last one is called binomial coefficient.

 

Example: duty calls

•There is an evil monster threatening the city.
•The mayor calls the Justice League.
•He requests that 3 members be sent to combat the menace.
•The Justice League draws 3 names out of a hat to decide.
•Does it matter who is selected first? NOPE
•Does it matter who is selected last? NOPE
 
 
 
Exercises:
 
1) We have 9 points in a plane and whatever three of them you choose, they aren't in a straight line. How many triangles can we form with these points?
 
2) An ice-cream seller has 12 different kind of flavours. If he sells ice-creams of two flavours, how many different ice-creams can he sell? And if the ice-creams had three flavours?
 
 
 
 
 
 
Solutions: 1) 84; 2) 66; 220

 

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