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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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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10
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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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If C(n, 7) = C(n, 5), find n
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3
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Three chairs are arranged in a row facing three other chairs. 4 boys and 2 girls are to be seated on these chairs such that girls are always facing each other. In how many ways can they be seated?
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5
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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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6
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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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7
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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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8
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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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9
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If A, B and C are mutually exclusive and exhaustive events of a random experiment such that P(B)=3/2P(A) and P(C)=1/2P(B), then P(A∪C)=
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