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

Algebra ->  Probability-and-statistics -> 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      Log On


   

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) About Me  (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,
N%5B1%5D=C%2812%2C8%29=495
For the second calculation, you have 10 slots to fill with 12 remaining questions since 1 and 2 are not allowed.
N%5B2%5D=C%2812%2C10%29=66
There is no overall or double counted since the groups are mutually exclusive.
So then,
N=N%5B1%5D%2BN%5B2%5D
N=495%2B66
N=561