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?
96
72
144
120
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A number lock on a suitcase has 3 wheels each labeled with 10 digits from 0 to 9. If the opening of the lock is a particular sequence of three digits with no repeats, how many such sequences will be possible?
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2
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A polygon has 44 diagonals. What is the number of its sides?
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3
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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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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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5
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In how many ways can a cricketer can score 200 runs with fours and sixes only?
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6
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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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7
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If 18Cr = 18Cr+2 ; find rC5.
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8
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Ten participants are participating in a competition. In how many ways can the first three prizes be won?
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9
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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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10
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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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