The students in a class are seated, according to their marks in the previous examination. Once, it so happens that four of the students got equal marks and therefore the same rank. To decide their seating arrangement, the teacher wants to write down all possible arrangements one in each of separate bits of paper in order to choose one of these by lots. How many bits of paper are required?
24
12
36
48
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Three unbiased coins are tossed. What is the probability of getting at most two heads ?
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2
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A polygon has 44 diagonals. What is the number of its sides?
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3
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How many natural numbers can be made with digits 0, 7, 8 which are greater than 0 and less than a million?
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4
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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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5
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In how many ways can the letters of the word 'LEADER' be arranged?
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6
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Six boys and 4 girls are to be seated in two separate rows with five chairs each, such that two particular girls are always together and all the girls are not in the same row. In how many ways can they be seated?
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7
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In how many ways can a group of 5 men and 2 women be made out of a total of 7 men and 3 women?
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8
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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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9
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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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10
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A basketball team of 5 players is to be selected from a group of 10 men and 8 women players. A volley ball team of 6 players is to be selected from a group of 8 men and 7 women players. Find the difference in the number of ways in which both the teams are selected, given that each team has only 2 female players.
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