SOLUTION: Seven orchids from a collection of 23 are to be selected for a flower show. Complete parts​ (a) and​ (b) below a) In how many ways can this be​ done? b.) How many ways ca

Algebra ->  Permutations -> SOLUTION: Seven orchids from a collection of 23 are to be selected for a flower show. Complete parts​ (a) and​ (b) below a) In how many ways can this be​ done? b.) How many ways ca      Log On


   



Question 1149279: Seven orchids from a collection of 23 are to be selected for a flower show. Complete parts​ (a) and​ (b) below
a) In how many ways can this be​ done?
b.) How many ways can the 7 be selected if 3 special plants from the 23 must be​ included?

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

(a)  Seven items can be selected from 23 different items by  C%5B23%5D%5E7 ways


         C%5B23%5D%5E7 = %2823%2A22%2A21%2A20%2A19%2A18%2A17%29%2F%281%2A2%2A3%2A4%2A5%2A6%2A7%29 = 245157 ways.


     It is the number of COMBINATIONS in this case.




(b)  In this case you are allowed to select only 7-3=4 items from 23-3 = 20 items.


     It can be done by  C%5B20%5D%5E4  ways.


     This time, calculate the value ON YOUR OWN.


     Happy calculations (!)

Solved.

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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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