SOLUTION: Amy and Bill are two of the 10 people joining a massive online game. If two people are to be selected at random as group leaders, find the probability that both Amy and Bill are s

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Question 1190820: Amy and Bill are two of the 10 people joining a massive online game. If two people are to be selected at random as group leaders, find the probability that both Amy and Bill are selected.
Answer by ikleyn(52864) About Me  (Show Source):
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Amy and Bill are two of the 10 people joining a massive online game.
If two people are to be selected at random as group leaders, find the probability
that both Amy and Bill are selected.
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In all, there are  C%5B10%5D%5E2 = %2810%2A9%29%2F2 = 45 possible pairs that can be selected as leaders.


Of these 45 pairs, only one pair is (Amy,Bill).


So the probability that the pair (Amy,Bill) is selected, equals  1%2F45.    ANSWER

Solved.

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This problem is on COMBINATIONS.


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.