A, B, C, and D are four points, any three of which are non-collinear. Then, the number of ways to construct three lines each joining a pair of points so that the lines do not form a triangle is
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1
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What is the sum of all 4 digit numbers that can be formed by the digits 1, 2, 3, 4 each exactly once
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2
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A number lock on a suitcase has 3 wheels each labeled with 10 digits from 0 to 9. If the opening of the lock is a particular sequence of three digits with no repeats, how many such sequences will be possible?
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3
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A fair coin is tossed 5 times. What is the probability of getting at least three heads on consecutive tosses?
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4
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From among the 36 students in a class, one leader and one class representative are to be appointed. In how many ways can this be done?
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5
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There are 6 letters for 3 envelopes. In how many different ways can the envelopes be filled?
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6
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How many rectangles can be formed out of a chess board ?
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7
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A polygon has 44 diagonals. What is the number of its sides?
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8
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The number of triangles that can be formed by choosing the vertices from a set of 12 points, seven of which lie on the same straight line, is
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9
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A teacher has to choose the maximum different groups of three students from a total of six students. Of these groups, in how many groups there will be included in a particular student?
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10
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Seven different objects must be divided among three people. In how many ways can this be done if one or two of them must get no objects?
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