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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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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2
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How many 5 digit even numbers with distinct digits can be formed using the digits 1, 2, 5, 5, 4?
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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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4
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How many parallelograms will be formed if 7 parallel horizontal lines intersect 6 parallel vertical lines?
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5
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In how many ways can 10 people line up at a ticket window of a railway station?
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6
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A, B, C, D and E sit on five chairs all of which are facing north. C will sit only on the leftmost chair and B will not sit anywhere to the left of A. In how many ways they can be seated?
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7
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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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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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A fair coin is tossed 5 times. What is the probability of getting at least three heads on consecutive tosses?
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10
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One red flower, three white flowers, and two blue flowers are arranged in a line such that
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