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  4. Person wishes to make up as many different parties as he can out of his 20 friends such that each party consists of the same number of persons. The number of friends he should invite are ..A.... . Here, A refers to

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Q. Person wishes to make up as many different parties as he can out of his 20 friends such that each party consists of the same number of persons. The number of friends he should invite are ..A.... . Here, A refers to

Permutations and Combinations

Solution:

Suppose he invites $r$ friends at a time.
Then, number of parties $={ }^{20} C_r$
And we know ${ }^n C_r$ is maximum for $r=\frac{n}{2}$, when $n$ is even.
Hence, he should invites 10 friends at a time, in order to have maximum parties.