Vivek has 31 friends. He wants to invite some of them in a manner that he can throw maximum number of parties; also each party should have same number of guests and different set of persons. How many parties can Vivek throw?

³¹C₁₅

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31!

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³¹C₁₇

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15!

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Solution

The correct option is A ³¹C₁₅
Soln:

As n is odd, $^{n} C_{r}$ is maximum when r = $\frac{(n - 1)}{2}$ =15 or $\frac{(n - 1)}{2}$ = 16.

So, number of parties possible $=^{31} C_{16} =^{31} C_{15} .$

Hence option (a)

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Vivek has 31 friends. He wants to invite some of them in a manner that he can throw maximum number of parties; also each party should have same number of guests and different set of persons. How many parties can Vivek throw?

The correct option is A 31C15Soln: As n is odd, nCris maximum when r = (n−1)2 =15 or (n−1)2 = 16. So, number of parties possible= 31C16=31C15. Hence option (a)

The correct option is A ³¹C₁₅
Soln:

As n is odd, $^{n} C_{r}$ is maximum when r = $\frac{(n - 1)}{2}$ =15 or $\frac{(n - 1)}{2}$ = 16.

So, number of parties possible $=^{31} C_{16} =^{31} C_{15} .$

Hence option (a)