Answer :
The four matches can be sequenced in 1350 different ways, ensuring that each player gets to play at least once.
What is a sequence?
A sequence is an enumerated collection of things in mathematics where repetitions are allowed and order is important. It includes members, much like a set (also called elements, or terms). A sequence can be formalized as a function from natural numbers (the positions of sequence elements) to the elements at each place. An indexed family, which is a function from any index set, can be thought of as a generalization of the concept of a sequence.
The final matches can be between any two players after we have made sure that every player has played at least one match (except those three matches played)
We can select any two players from a pool of six for the first game =[tex]6_{c_{2} }[/tex]
We can select either of the two players from a total of four for the second match is [tex]4_{c_{2} }[/tex]
We have a choice of two players for the third game.=[tex]2_{c_{2} }[/tex]
Any of the two players from the pool of six can be selected for the fourth match= [tex]6_{c_{2} }[/tex]
P(x) =[tex]6_{c_{2} }[/tex]×[tex]4_{c_{2} }[/tex] ×[tex]2_{c_{2} }[/tex] × [tex]6_{c_{2} }[/tex]
P(x) = 15 × 6 × 1 × 15
P(x) = 1350
Therefore, the four matches can be arranged in 1350 different ways, ensuring that each player gets to play at least once.
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