Combinations of 6 taken 4 at a time

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SUMMARY

The calculation of combinations, specifically 6C4, results in 15 distinct sets when order is not considered. However, if the requirement is for all sets to be distinct, the interpretation of combinations changes. The discussion clarifies that 6C4 is calculated as 6!/(4!*2!) which equals 15, while permutations, represented as 6P4, yield 360 distinct arrangements. The distinction between combinations and permutations is crucial, as it determines whether order matters in the selection process.

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the calculation 6C4 shows 15 but what if all sets are to be distinct?
the calculation 6C4 shows 15 but what if all sets are to be distinct? meaning 1,2,3,4 is the same as 4,3,2,1. I made a tree diagram and i get 10... assuming i did that correctly...?
 
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Vector1962 said:
Summary:: the calculation 6C4 shows 15 but what if all sets are to be distinct?

the calculation 6C4 shows 15 but what if all sets are to be distinct? meaning 1,2,3,4 is the same as 4,3,2,1. I made a tree diagram and i get 10... assuming i did that correctly...?
There are definitely 15 distinct combinations. It's easier to count all the ways of leaving two numbers out.
 
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6C4 is the number of combinations, meaning that order does not matter. 6P4 is the number of permutations, meaning that order does matter.
6C4 = 6!/(4!*2!) = 30/2=15.
6P4 = 6!/2! = 720/2 = 360.
The extra 4! in the denominator of 6C4 divides by the number of ways that the 4 selected can be ordered, so the result is the number of possibilities ignoring their order.
 
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