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Permutations and Combinations
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A person wishes to make as many different parties as he can out of 10 of his friends. Each party consist of same no. of friends. Out of these parties in how many parties a particular friend will be found?
jeemain
math
class11
ch7
permutations-and-combinations
combinations
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asked
Aug 31, 2013
by
rvidyagovindarajan_1
edited
Aug 5, 2014
by
sharmaaparna1
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$^nC_r$ is maximum if $r=\large\frac{n}{2}$ or $r=\large\frac{n+1}{2}$
Let him invite $r$ friends at a time in each party.
Then the number of parties = $^{10}C_r$
This is maximum only if $r=5$
Out of these $ ^{10}C_5$ parties a particular person can be found in
$^9C_4 =126$ parties.
This is because out of any 5 friends 1 particular friend is included and the
remaining 4 friends are to be selected from remaining 9 friends.=$^9C_4$ (ways.)
answered
Aug 31, 2013
by
rvidyagovindarajan_1
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