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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1
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How many natural numbers can be made with digits 0, 7, 8 which are greater than 0 and less than a million?
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2
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Two variants of the CAT paper are to be given to 12 students. In how many ways can the students be placed in two rows of six each so that there should be no identical variants side by side and that the students sitting one behind the other should have the same variant. Find the number of ways this can be done
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3
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In how many different ways can the letters of the word 'OPTICAL' be arranged so that the vowels always come together?
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4
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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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5
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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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6
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How many words can be formed from the letters of the word "SIGNATURE" so that vowels always come together.
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7
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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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8
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The number of circles that can be drawn out of 10 points of which 7 are collinear is
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9
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If a team of 4 persons is to be selected from 8 males and 8 females, then in how many ways can the selections be made to include at least 1 female
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10
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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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