Math combinations problem

[baywatch123]

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For new car purchases, an automobile company allows the selection of two free “extras” from a list of seven. How many different ways can a car be customized with extras?

the answer is 21, how would you even approach this question... my first line of thought when i see "how many ways" is to think of combinations... but clearly that doesn't work here

please help??

 

[TD21]

7x6=42. Ask yourself, does it matter if you custmoze w/ part 7 then part 6, or part 6 then part 7? no, so it is a combination problem, not permutation, and you divide by 2!, which is 2x1 . So answer is 21

 

[baywatch123]

7x6=42. Ask yourself, does it matter if you custmoze w/ part 7 then part 6, or part 6 then part 7? no, so it is a combination problem, not permutation, and you divide by 2!, which is 2x1 . So answer is 21

why 7x6? and then divide by 2? srry it's late in the night and im just reviewing my past corrected exams

 

[TD21]

Because there are 7 possibilities for first "extra," and there are 6 possibilities for the second "extra." This is what you always do first whether permutation or combinations. Then I ask myself if order matters, and since it does not matter, I know I have to divide 42 by some number to make it smaller, and the number you divide by is 2 factorial Srry if this doesn't make sense, I do things this way so I can half logic stuff out w/o having to completely remember the formulas. maybe someone else can give a better explanation.

 

[virajpatel]

I disagree I think this is a combination problem you may have set it up wrong because when I calculate 7C2 I get 21.

 

[virajpatel]

You are SELECTING r (2 extras) objects out of n (7 extras), you are not arranging them differently. the keyword that triggers combination is 'selection'. If the word was replaced by 'arrangement' then you would refer to permutation.

 

[baywatch123]

You are SELECTING r (2 extras) objects out of n (7 extras), you are not arranging them differently. the keyword that triggers combination is 'selection'. If the word was replaced by 'arrangement' then you would refer to permutation.

ah okay so i was partially correct

thank you, and thank you to everyone else