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?
63
90
126
45
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1
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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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How many parallelograms will be formed if 7 parallel horizontal lines intersect 6 parallel vertical lines?
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2
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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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3
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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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4
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In a lottery, there are 10 prizes and 25 blanks. A lottery is drawn at random. What is the probability of getting a prize?
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5
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A speaks truth in 75% cases and B in 80% of the cases. In what percentage of the cases are they likely to contradict each other, narrating the same incident?
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6
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What is the probability of getting at least one six in a single throw of three unbiased dice?s
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7
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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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8
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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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9
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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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