The number of triangles that can be formed by choosing the vertices from a set of 12 points, seven of which lie on the same straight line, is
185
175
115
105
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1
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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?
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2
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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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3
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There are 6 letters for 3 envelopes. In how many different ways can the envelopes be filled?
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4
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One card is drawn at random from a pack of 52 cards. What is the probability that the card drawn is not a face card (Jack, Queen and King only)?
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5
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A committee of 8 members is to be selected from a group of 12 male and 10 female members. In how many ways the committee is selected such that at most two and at least one male member are there in the committee?
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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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How many parallelograms will be formed if 7 parallel horizontal lines intersect 6 parallel vertical lines?
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8
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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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9
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A five-letter word is to be formed from a group of 5 vowels and 4 consonants, using at least one vowel and at least one consonant. In how many ways the word having a greater number of consonants than vowels can be formed?
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10
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A basketball team of 5 players is to be selected from a group of 10 men and 8 women players. A volley ball team of 6 players is to be selected from a group of 8 men and 7 women players. Find the difference in the number of ways in which both the teams are selected, given that each team has only 2 female players.
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