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

Algebra ->  Permutations -> 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       Log On


   



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(52776) About Me  (Show Source):
You can put this solution on YOUR website!
.

(1)  In  C%5B40%5D%5E8 ways.


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


     C%5B40%5D%5E8 = 40%21%2F%288%21%2A32%21%29 = %2840%2A39%2A38%2A37%2A36%2A35%2A34%2A33%29%2F%281%2A2%2A3%2A4%2A5%2A6%2A7%2A8%29 = 76904685  ways.          ANSWER



(2)  For a party of n participants, the number of handshakes is  C%5Bn%5D%5E2 = %28n%2A%28n-1%29%29%2F2.


     For n= 30 participants, the number of handshakes is  %2830%2A29%29%2F2 = 435.       ANSWER

Solved.

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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.