SOLUTION: . An instructor gives an exam with fourteen questions. Students are allowed to choose any ten to answer.
a. How many different choices of ten questions are there?
b. Suppose six
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-> SOLUTION: . An instructor gives an exam with fourteen questions. Students are allowed to choose any ten to answer.
a. How many different choices of ten questions are there?
b. Suppose six
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Question 1173947: . An instructor gives an exam with fourteen questions. Students are allowed to choose any ten to answer.
a. How many different choices of ten questions are there?
b. Suppose six questions require proof and eight do not.
(i) How many groups of ten questions contain four that
require proof and six that do not?
(ii) How many groups of ten questions contain at least
one that requires proof? Answer by VFBundy(438) (Show Source):
You can put this solution on YOUR website! How many different choices of ten questions are there?
14C10 = = 1001
---------------------------------------------- How many groups of ten questions contain four that require proof and six that do not?
6C4 * 8C6 = * = 15 * 28 = 420
---------------------------------------------- How many groups of ten questions contain at least one that requires proof?
All of them. (Or, 1001.) Since only eight questions do not require proof, that means there will always be at least two questions of the group of ten that do require proof.
