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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A, B, C, and D are four points, any three of which are non-collinear. 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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From among the 36 students in a class, one leader and one class representative are to be appointed. In how many ways can this be done?
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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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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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6
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How many parallelograms will be formed if 7 parallel horizontal lines intersect 6 parallel vertical lines?
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7
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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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8
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In how many ways the letters of the word “UNDERDOG” can be arranged such that the first and last letters are same and no two vowels are together?
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9
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How many rectangles can be formed out of a chess board ?
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10
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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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