In how many different ways can the letters of the word 'OPTICAL' be arranged so that the vowels always come together?
120
720
4320
2160
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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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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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3
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If C(n, 7) = C(n, 5), find n
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4
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There are 20 people among whom two are sisters. Find the number of ways in which we can arrange them around a circle so that there is exactly one person between the two sisters.
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5
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If (n + 2)! = 2550 (n!); find ’n’
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6
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What is the sum of all 4 digit numbers that can be formed by the digits 1, 2, 3, 4 each exactly once
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7
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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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8
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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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9
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How many integers between 1000 and 10000 have no digits other than 4, 5, or 6?
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10
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In a single throw with four dice,the probability of throwing seven is
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