A 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. How many friends should he invite ?

10

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15

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20

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25

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Solution

The correct option is A $10$
Suppose he invites r friends at a time.

Then the total number of parties is $20_{C_{r}}$ .

We have to find the maximum value of $20_{C_{r}}$ which is for $r = 10$ , because $n_{C_{r}}$ is maximum for $r = n / 2$ , when n is even.

Hence, he should invite 10 friends at a time in order to form the maximum number of parties.

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