SOLUTION: Counting Methods A company has 12 male and 10 female employees, and needs to nominate 3 men and 3 women for the company bowling team. How many different teams can be formed?

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Question 1061927: Counting Methods A company has 12 male and 10 female employees, and needs to nominate 3 men and 3 women for the company bowling team. How many different teams can be formed?
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Counting Methods A company has 12 male and 10 female employees, and needs to nominate 3 men and 3 women for the company bowling team.
How many different teams can be formed?
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Answer. C%5B12%5D%5E3.C%5B10%5D%5E3 = 220*120 different teams can be formed.

Solution

You can choose 3 men of 12 by C%5B12%5D%5E3 ways = %2812%2A11%2A10%29%2F%281%2A2%2A3%29 = 2*11*10 = 220 ways.

You can choose 3 women of 10 by C%5B10%5D%5E3 ways = %2810%2A9%2A8%29%2F%281%2A2%2A3%29 = 10*3*4 = 120 ways.

You can then combine men and women by 220*120 ways.


On Combinations, see the 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".