-5,-3,-1,1,3,5
If a and b are different integers chosen from the list above, how many possible values are there of the product ab? I know the answer is 15 but do I always use factorial method whenever I meet questions that ask for how many possibilitites? And the factorial is always 1 less than the total number of terms?
To obtain the product ab, you are simply choosing pairs of numbers form the 6 different numbers.
e.g. (3,-5), (1,-1) etc
that would be 6x5 or 30
but isn't (5,3) the same product as (3,5), and don't we have a double choice for each pair like that ?
so the number of possible pairs to form ab is 15
or
choosing any 2 from 6 is C(6,2 ) = 15
Your question "how many possible values are there of the product ab?" is a bit ambigious.
I read it as how many different numbers could we use to form the product ab
Somebody could interpret it as how many different results do you get?
In that case you would have to rethink the solution, since there is further duplication.
e.g. choosing -3,-5 yields the result 15
but 3,5 also yields the result 15
So do we just divide our answer of 15 by 2 ?
But that does not divide evenly, thus 7.5 would not make any sense.
I will let you think about that .