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)=
3/13
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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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2
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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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3
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From a pack of 52 playing cards, two cards are drawn together at random. Calculate the probability of both the cards being the Kings.
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4
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In how many different ways can the letters of the word 'DETAIL' be arranged in such a way that the vowels occupy only the odd positions?
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5
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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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6
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If ^{18}C_{r }= ^{18}C_{r+2 }; find ^{r}C_{5}.
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There are seven pairs of black shoes and five pairs of white shoes. They are all put into a box and shoes are drawn one at a time. To ensure that at least one pair of black shoes are taken out, what is the number of shoes required to be drawn out?
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8
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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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9
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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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10
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Two dice are thrown simultaneously. What is the probability of getting two numbers whose product is even?
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