SOLUTION: A teacher has 20 boys and 10 girls in her class. In how many way can she select 6 of the children to be in a play if she must have 3 boys and 3 girls?

Question 1173263: A teacher has 20 boys and 10 girls in her class. In how many way can she select 6 of the children to be in a play if she must have 3 boys and 3 girls?
Answer by ikleyn(52781) (Show Source): You can put this solution on YOUR website!
.


The teacher can choose 3 boys from 20 boys by   =  = 1140 ways.


The teacher chooses 3 girls from 10 girls by   =  = 120 ways.


Since the selections in each category are independent, the entire choice can be done in  1140*120 ways =  136800 ways.    ANSWER

Solved.

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This problem is on COMBINATIONS.

So, you should know what the combinations are and how to calculate them.

You can learn about it from these introductory lessons on combinations
On Combinations, see introductory lessons
    - Introduction to Combinations
    - PROOF of the formula on the number of Combinations
    - Problems on Combinations
    - Fundamental counting principle problems
    - 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.

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

If you will come to the forum with new problems on PERMUTATIONS and COMBINATIONS,

please report me whether you are familiar with basic conceptions and methods of calculations

and whether you just have read that lessons I recommended you.

Good luck (!)   and   Happy learning (!)

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