SOLUTION: In how many ways can you select 4 essay questions out of 10? I just need a basic formula to begin this problem! Thanks....
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Question 584053: In how many ways can you select 4 essay questions out of 10? I just need a basic formula to begin this problem! Thanks....
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
It depends on whether order matters. That is, is Q1, Q2, Q3, Q4 the same or different from Q2, Q1, Q3, Q4?
If order matters, that is if the two examples given above are actually considered different selections, then you want 
where 
is calculated by !})
. The idea being, in your example, that there are 10 ways to pick the first question and for each of these 10 ways there are 9 ways to pick the second question, so 10 times 9, and then for those 90 ways there are 8 ways to pick the third question, and so on. The math is thus:
On the other hand, if order doesn't matter, using the above arithmetic overcounts by a factor of the number of ways you can arrange 4 things, namely 4!. Hence, if order doesn't matter you need another factor in the denominator: You want 
where 
is calculated by !})
.
And the arithmetic for your problem becomes:
(6\ \times\ 5\ \times\ 4\ \times\ 3\ \times\ 2)}\ =\ \frac{10\ \times\ 9\ \times\ 8\ \times\ 7}{4\ \times\ 3\ \times\ 2}\ =\ 5\ \times\ 3\ \times\ 2\ \times\ 7)
John
My calculator said it, I believe it, that settles it
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