SOLUTION: 1. From a class of 40 students 8 students will be chosen to join the science field trip. In how many ways can the student be chosen? 2. In a gathering, the host makes sure that

Question 1178812: 1. From a class of 40 students 8 students will be chosen to join the science field trip. In how many ways can the student be chosen?
2. In a gathering, the host makes sure that each guests shakes hands with everyone else. If there are 30 guests, how many handshakes will be done?
Answer by ikleyn(52777) (Show Source): You can put this solution on YOUR website!
.


(1)  In   ways.


     It is the number of COMBINATIONS of 40 students taken 8 at a time.


      =  =  = 76904685  ways.          ANSWER



(2)  For a party of n participants, the number of handshakes is   = .


     For n= 30 participants, the number of handshakes is   = 435.       ANSWER

Solved.

---------------

Both problems are on COMBINATIONS.

On Combinations, see introductory lessons
    - Introduction to Combinations
    - PROOF of the formula on the number of Combinations
    - Problems 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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