B Combinations of 6 taken 4 at a time

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The calculation of 6C4 yields 15 combinations, indicating that order does not matter. When considering distinct sets, the tree diagram approach mistakenly suggests there are only 10 combinations. The correct interpretation involves recognizing that 6C4 accounts for all unique groupings of four numbers from a set of six. The formula 6C4 = 6!/(4!*2!) confirms the result of 15 by factoring out the permutations of the selected numbers. Thus, the total number of distinct combinations remains 15.
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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.
 
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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