SOLUTION: A student must answer 7 questions on a 12 question test. How many ways can a student do this, and how many ways are there if the student must answer the first and last questions?

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Question 1155078: A student must answer 7 questions on a 12 question test. How many ways can a student do this, and how many ways are there if the student must answer the first and last questions?
Answer by ikleyn(52786)   (Show Source): You can put this solution on YOUR website!
.

The student can select 7 questions from 12 questions by   ways.


It is the number of combinations of 12 items taken 7 at a time.


 =  = .


Calculate it using your calculator.

Answered, and you are instructed and directed.

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On Combinations,  see the lessons
    - Introduction to Combinations
    - PROOF of the formula on the number of Combinations
    - Problems on Combinations
    - Math circle level problem on Combinations
    - OVERVIEW of lessons on Permutations and Combinations
in this site.

Also,  you have this free of charge online textbook in ALGEBRA-II in this site
    - ALGEBRA-II - YOUR ONLINE TEXTBOOK.

The referred lessons are the part of this online textbook under the topic  "Combinatorics: Combinations and permutations".


Save the link to this textbook together with its description

Free of charge online textbook in ALGEBRA-II
https://www.algebra.com/algebra/homework/complex/ALGEBRA-II-YOUR-ONLINE-TEXTBOOK.lesson

into your archive and use when it is needed.


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