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How many different committees of 5 can be formed from 6 men and 4 women on which exact 3 men and 2 women serve?

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The number of ways in which a host lady can invite for a party of 8 out of 12 people of whom two do not want to attend the party together is

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Given 11 points, of which 5 lie on one circle, other than these 5, no 4 lie on one circle. Then the number of circles that can be drawn so that each contains at least 3 of the given point is

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If , then the value of r is

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The number of diagonals that can be drawn by joining the vertices of an octagon is