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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1
Discuss

The value of ^{75}P_{2}
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2
Discuss

Three unbiased coins are tossed. What is the probability of getting at most two heads ?
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3
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A, B, C, and D are four points, any three of which are noncollinear. 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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4
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A committee of 8 members is to be selected from a group of 12 male and 10 female members. In how many ways the committee is selected such that at most two and at least one male member are there in the committee?
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5
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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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6
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A speaks truth in 75% cases and B in 80% of the cases. In what percentage of the cases are they likely to contradict each other, narrating the same incident?
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7
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A, B, C, D and E sit on five chairs all of which are facing north. C will sit only on the leftmost chair and B will not sit anywhere to the left of A. In how many ways they can be seated?
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8
Discuss

Four letters are selected from the word “CAPAME” and are rearranged to form four letter words. How many words can be formed?
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9
Discuss

How many numbers can be formed from 1, 2, 3, 4, 5 (without repetition), when the digit at the unit’s place must be greater than that in the ten’s place?
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10
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In a lottery, there are 10 prizes and 25 blanks. A lottery is drawn at random. What is the probability of getting a prize?
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