Permutations & Combinations Questions (855)

Consider the convex polygon, which has 35 diagonals. Match the following lists and choose the correct code.List IList IIa. Number of triangles joining the vertices of the polygonp. 210b. Number of points of intersections of diagonal which lies inside the polygonq. 120c. Number of triangles in which exactly one side is common with that of polygonr. 10d. Number of triangles in which exactly two sides are common with that of polygons. 60Codes:abcd(1)qpsr(2)rqps(3)srqp(4)prsq

Find the maximum number of points of intersection of 7 straight lines and 5 circles when 3 straight lines are parallel and 2 circles are concentric.

If \({}^{15}C_{3r} : {}^{15}C_{r+1} = 11:3\), find the value of r.

(b) If \({}^{56}P_{r+6} : {}^{54}P_{r+3} = 30800:1\), find \(r\).

Let $n$ be the number of ways in which 5 boys and 5 girls can stand in a queue such that all girls stand consecutively. Let $m$ be the number of ways such that exactly four girls stand consecutively. Then $\dfrac{m}{n}$ is