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.Com
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(52777)   (Show Source): You can put this solution on YOUR website!
.

(a)  Seven items can be selected from 23 different items by   ways


          =  = 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    ways.


     This time, calculate the value ON YOUR OWN.


     Happy calculations (!)

Solved.

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

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.


/\/\/\/\/\/\/\/

Do not forget to submit your "THANKS" to me (!)



RELATED QUESTIONS

Seven orchids from a collection of 23 are to be selected for a flower show. Complete... (answered by ikleyn)
A survey of flower gardeners showed the following: 45 grew roses 7 grew both... (answered by Edwin McCravy)
a survey of flower gardeners showed the following: 87 grew roses, 27 grew tulips, 26... (answered by Theo)
A survey of flower gardeners showed the following: 45 grew roses 7 grew both... (answered by edjones)
According to Masterfoods, the company that manufactures M&M’s, 12% of peanut M&M’s... (answered by ikleyn)
A group consists of five men and seven women. Four people are selected to attend a... (answered by edjones)
For the given pair of events A and​ B, complete parts​ (a) and​ (b)... (answered by Boreal)
A survey of flower gardeners showed the following: 45 grew roses 7 grew both... (answered by josmiceli)
A group consists of seven men and eight women. Three people are selected to attend a... (answered by jim_thompson5910)