A person wishes to make up as many different parties as he can out 20 friends, each party consisting of the same number. How many should he invite at a time? In how many of these would the same man be found?

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Solution

Since $n = 20$ is even, $^{20} C_{r}$ is greatest when $r = \frac{20}{2} = 10$ .
Hence the maximum number of parties $=^{20} C_{10}$ . Thus he should invite 10 friends at a time in order to form the max number of parties. Also the same man will be found in $^{19} C_{9}$ parties.

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A person wishes to make up as many different parties as he can out 20 friends, each party consisting of the same number. How many should he invite at a time? In how many of these would the same man be found?

Since n=20 is even, 20Cr is greatest when r=202=10.Hence the maximum number of parties =20C10. Thus he should invite 10 friends at a time in order to form the max number of parties. Also the same man will be found in 19C9 parties.

Since $n = 20$ is even, $^{20} C_{r}$ is greatest when $r = \frac{20}{2} = 10$ .
Hence the maximum number of parties $=^{20} C_{10}$ . Thus he should invite 10 friends at a time in order to form the max number of parties. Also the same man will be found in $^{19} C_{9}$ parties.