In a group of 6 boys and 4 girls, four children are to be selected. In how many different ways can they be selected such that at least one boy should be there?
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1
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It is required to seat 5 boys and 4 girls in a row so that the girls occupy the even places. How many such arrangements are possible?
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2
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How many rectangles can be formed out of a chess board ?
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3
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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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4
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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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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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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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7
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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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8
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In how many ways the letters of the word “UNDERDOG” can be arranged such that the first and last letters are same and no two vowels are together?
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9
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How many 4-letter words with or without meaning, can be formed out of the letters of the word, 'LOGARITHMS', if repetition of letters is not allowed?
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10
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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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