A person tries to form as many different parties as he can, out of his 20 friends. In how many of these parties would the same friends be found?

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Solution

If a person forms a party of $n$ friends out of his $20$ friends

then the number of parties possible $=^{20} C_{n}$
To maximize $^{20} C_{n}, n$ must be $= \frac{20}{2} = 10$
$∴$ number of parties $=^{20} C_{10}$

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A person tries to form as many different parties as he can, out of his 20 friends. In how many of these parties would the same friends be found?

If a person forms a party of n friends out of his 20 friendsthen the number of parties possible =20CnTo maximize 20Cn,n must be =202=10∴ number of parties =20C10

If a person forms a party of $n$ friends out of his $20$ friends

then the number of parties possible $=^{20} C_{n}$
To maximize $^{20} C_{n}, n$ must be $= \frac{20}{2} = 10$
$∴$ number of parties $=^{20} C_{10}$