SOLUTION: An instructor gives an exam with fourteen questions. Students are allowed to choose any ten to answer. Suppose the exam instructions specify that either both questions 1 and 2 a

Question 1062946: An instructor gives an exam with fourteen questions. Students are allowed to choose any ten to answer.
Suppose the exam instructions specify that either both questions 1 and 2 are to be included among the ten or neither is to be included. How many diﬀerent choices of ten questions are there?
Answer by Fombitz(32388) (Show Source): You can put this solution on YOUR website!
For the first calculation, you have 8 slots to fill with the remaining 12 questions since 1 and 2 are already chosen,

For the second calculation, you have 10 slots to fill with 12 remaining questions since 1 and 2 are not allowed.

There is no overall or double counted since the groups are mutually exclusive.
So then,

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