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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Two cards are drawn together from a pack of 52 cards. The probability that one is a spade and one is a heart, is
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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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A person tosses an unbiased coin. When head turns up, he gets Rs.8 and tail turns up he loses Rs.4. If 3 coins are tossed, what is probability that he gets a profit of Rs.12?
SolutionPerson will get profit of Rs 12 only when there is 2H (Head) and 1T (Tail) H + H + T = 12 8 + 8 + (-4) = 12 Total outcome of 2 head and 1 tail = 23 = 8 i.e (T, H, TH, HT, HH, HHT, HTH, THH) Total event with 2H and 1 T is 3 therfore probability = 3/8 |
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In how many different ways can the letters of the word 'OPTICAL' be arranged so that the vowels always come together?
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5
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A box contains two white balls, three black balls and four red balls. Balls of the same colour are distinct. The number of ways in which three balls can be drawn from the box if atleast one black ball is to be included in the draw, is
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6
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What is the probability of getting at least one six in a single throw of three unbiased dice?s
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7
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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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8
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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?
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A biased coin in tossed thrice. What is the probability that heads turns out at least twice considering that the probability of a head is 60%?
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10
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There are 8 orators A, B, C, D, E, F, G, and H. In how many ways can the arrangements be made so that A always comes before B and B always comes before C.
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