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A person tries to form as many different parties as he can, out of his20 friends. Each party should consist of the same number. How many friendsshould be invited at a time? In how many of these parties would the samefriends be found? |
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Answer» Let the person invite r number of friends at a time. Then, the number of parties is `.^(20)C_(r )`, which is maximum when r=10. Ifa particular friend will be found in x parties, then x is the number of combinations out of 20 in which this particular friend must be included. Therefore, we have to select 9 more from 19 remaining friends. Hence, `x= .^(19)C_(9)`. |
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