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Higher Study | Mathematics | Combinatorics

 How many friends are there In a group of 267 people, who have an identical number of friends in the group?
If 7 points are chosen inside or on the unit circle, then How many points are there which are at a distance at most 1 unit?
How many integers are atleast consecutive if 51 numbers are chosen from the integers between 1 and 100 inclusively?
How many numbers must be selected from the set {1, 2, 3, 4, 5, 6} to guarantee that at least one pair of these numbers add up to7?
What is the maximum number of regions that the plane R2 can be partitioned into using 10 lines?
In a group of 6 people which of the following can be a possibility: (According to the Pigeonhole principle)
If there are more than m objects and there are m pigeonholes then: Which of the following is true?
How many cards must be picked from a standard pack of 52 cards to surely get 3 cards of the same suit? (Club, Diamond, Heart and Spade are the suits.)
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