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How many rounds of matches does a knock out tennis tournament have if it starts with 64 players and every player needs to win 1 match to move at the next round?

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Important Questions on Permutations and Combinations

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There are N men sitting around a circular table at N distinct points. Every possible pair of men except the ones sitting adjacent to each other sings a two minute song one pair after other. If the total time taken is 88 minutes, then what is the value of N?

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in a class with boys and girls a chess competition was played wherein every student had to play one game with every other student. It was observed that in 36 matches both the players were boys and in 66 matches both were girls. What is the number of matches in which one boy and one girl play against each other?
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Zada has to distribute 15 chocolates among five of her children Sana, Ada, Jiya, Amir and Farhan. She has to make sure that Sana gets at least 3 chocolate and at most 6 chocolates. In how many ways can this be done if each child gets at least one chocolate?
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Mr. Shah has to divide his assets worth 30 crores in three parts to be given to three of his sons Ajay, Vijay and Arun ensuring that every son gets assets atleast five crores. In how many ways, can this be done if it is given that the three sons should get their shares in multiple of 1 crore?

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Three variables x, y, z have a sum of 30. All three of them are non-negative integers. If any two variables don't have the same value and exactly one variable has a value of less than or equal to three, then find the number of possible solutions for the variables.
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The letters of the word ALLAHABAD are rearranged to form a new word and put in a dictionary. If the dictionary had only these words and one word on every page in alphabetical order then what is the page number on which the letter LABADALAH comes?
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If x, y and z can only take the values 1, 2, 3, 4, 5, 6, 7 then find the number of solutions of the equation x + y + z= 12.
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There are nine points in a plane such that no three are collinear. Find the number of triangles that can be formed using these points as vertices.