A person tries to form as many different parties as he can, out of his $20$ friends. Each party should consist of the same number. How many friends should be invited at a time? In how many of these parties would the same friends be found?

92378

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92364

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92376

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92391

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Solution

The correct option is A 92378
Let the person invite r number of friends at a time. Then, the number of parties is $^{20} C_{r}$ , which is maximum when $r = 10$ . If a 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, $x =$ $^{19} C_{9}$ =92378.

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A person tries to form as many different parties as he can, out of his 20 friends. Each party should consist of the same number. How many friends should be invited at a time? In how many of these parties would the same friends be found?

A person tries to form as many different parties as he can, out of his $20$ friends. Each party should consist of the same number. How many friends should be invited at a time? In how many of these parties would the same friends be found?