SOLUTION: hello how to i do this? . An instructor asks 12 questions on a test. The student is asked to select and
answer 10 of these questions. IN how many ways can the questions be
chos
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Question 855190: hello how to i do this? . An instructor asks 12 questions on a test. The student is asked to select and
answer 10 of these questions. IN how many ways can the questions be
chosen?
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
you want to know how many possible combinations of 10 questions out of 12 you can get where order is not important.
that would be the combination formula.
the combination formula is:
C(n,x) = n! / (x! * (n-x)!)
in your problem:
n = 12
x = 10
C(n,x) becomes C(12,10) which is equal to 12! / (10! * 2!)
this is equivalent to:
(12 * 11 * 10!) / (10! * 2!)
the 10! in the numerator and the 10! in the denominator cancel out and you are left with:
(12 * 11) / (2!) which is equivalent to:
(12 * 11) / 2
12 / 2 is equal to 6 so your equation becomes:
(6 * 11) which is equal to 66.
there are 66 possible ways in which the student can answer 10 out of 12 questions.
it's hard to show you how this work with so many questions.
i'll simplify the problem so i can show you how it works.
suppose 3 questions and you have to pick 2 out of the 3.
the same formula applies:
C(3,2) = 3! / (2! * 1!) which is equal to (3*2*1) / (2*1*1) which is equal to 3.
there are 3 possible ways 2 questions out of 3 can be answered.
those ways are:
let the 3 different ways be labeled abc.
you are picking 2 out of 3.
order doesn't matter.
you pick:
ab
ac
bc
there are no other ways because order doesn't matter so ba and ab would be considered the same 2 questions
if order did matter, then the equation would have been P(3,2) which is equal to 6 and the possible selections would have been:
ab
ba
ac
ca
bc
cb
note that ab and ba are the same questions only chosen in a different order.
i believe your problem is a combination type problem so the original equations i gave you would be correct.
these are the number of possible ways 10 questions can be chosen out of 12 questions when order doesn't matter which is the combination formula.
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