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In ;a plane, there are 5 straight lines which will pass through a givenpoint, 6 others which all pass through another given point, and 7 otherswhich all as through a third given point. Supposing no three lines intersectat any point and no two are parallel, find the number of triangles formed bythe intersection of the straight line. |
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Answer» Let 5 straight lines be passing through A, 6 passing through B, and 7 passing through C. In all, there are 18 straight lines. To find the number of triangles, we have to find the number of selection of 3 lines from these 18 lines, keeping in mind that selection of 3 lines from the lines passing through A, B, or C will not give any triangle. Hence, the required number of triangles is `.^(18)C_(3)-(.^(5)C_(3)+ .^(6)C_(3) + .^(7)C_(3))=751`. |
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