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?
60
54
51 / 3
2 x 4!
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1
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In how many different ways can the letters of the word 'MATHEMATICS' be arranged so that the vowels always come together
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2
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Ten participants are participating in a competition. In how many ways can the first three prizes be won?
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3
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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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4
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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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Two variants of the CAT paper are to be given to 12 students. In how many ways can the students be placed in two rows of six each so that there should be no identical variants side by side and that the students sitting one behind the other should have the same variant. Find the number of ways this can be done
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6
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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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7
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From a group of 7 men and 6 women, five persons are to be selected to form a committee so that at least three men are in the committee. In how many ways can it be done?
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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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10
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One card is drawn at random from a pack of 52 cards. What is the probability that the card drawn is not a face card (Jack, Queen and King only)?
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