.
It is your mistake to think that the order does matter in this problem.
It DOES NOT: the team (John,Martha,Peter) is THE SAME as the team (Peter,John,Martha).
Therefore, you should use COMBINATIONS.
You can select 2 different boys from 20 boys by = = 10*19 = 190 different ways.
You can select one girl from 16 girls by = 16 different ways.
Since the selections in different (disjoint) categories are independent, the total number of different teams is the product
. = 190*16 = 3040. ANSWER
Solved.
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You REALLY NEED to learn the basic knowledge in Combinatorics.
For introductory lessons on permutations and combinations, see
- Introduction to Permutations
- PROOF of the formula on the number of Permutations
- Simple and simplest problems on permutations
- Introduction to Combinations
- PROOF of the formula on the number of Combinations
- Problems on Combinations
- Miscellaneous problems on permutations, combinations and other combinatoric entities
- Fundamental counting principle problems
- Nice recreational problems on permutations
- OVERVIEW of lessons on Permutations and Combinations
in this site. // I listed here the "introductory" lessons only . . .
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.