118968 In how many ways 7 men and 7 women can be seated around a round table such that no two women can sit together
#[Qdiff: Hard, QCat: Numerical Based, examname: Now, [MHT CET-2021], no two women are to sit together as such the 7 women are to be arranged in seven empty seats between two consecutive men and number of arrangement will be 7 Hence, by fundamental theorem the total number ways \(=7 ! \times 6 !\), 65. A committee of 4 is to selected from 4 Engineers, 6 Doctors and 5 Lawyers. The number of ways in which there is at least one from each profession is,

118973 The number of ways in which the letters \(x_1\), \(\mathrm{x}_2, \ldots \mathrm{x}_{10,} \mathrm{y}_1, \mathrm{y}_2, \ldots \mathrm{y}_{15}\) can be arranged in a line such that the suffixes of \(x\) and those of \(y\) are in ascending order of magnitude is

118974 In a polygon no three diagonals are concurrent. If the total number of points of intersection of diagonals interior to the polygon be 70 , then the number of diagonals of the polygon, is

118975 Let \(\mathbf{T}_{\mathbf{n}}\) denote the number of triangles which can be formed using the vertices of a regular polygon of \(n\) sides. If \(T_{n+1}-T_n=21\), then \(n\) equals to

118968 In how many ways 7 men and 7 women can be seated around a round table such that no two women can sit together
#[Qdiff: Hard, QCat: Numerical Based, examname: Now, [MHT CET-2021], no two women are to sit together as such the 7 women are to be arranged in seven empty seats between two consecutive men and number of arrangement will be 7 Hence, by fundamental theorem the total number ways \(=7 ! \times 6 !\), 65. A committee of 4 is to selected from 4 Engineers, 6 Doctors and 5 Lawyers. The number of ways in which there is at least one from each profession is,

118973 The number of ways in which the letters \(x_1\), \(\mathrm{x}_2, \ldots \mathrm{x}_{10,} \mathrm{y}_1, \mathrm{y}_2, \ldots \mathrm{y}_{15}\) can be arranged in a line such that the suffixes of \(x\) and those of \(y\) are in ascending order of magnitude is

118974 In a polygon no three diagonals are concurrent. If the total number of points of intersection of diagonals interior to the polygon be 70 , then the number of diagonals of the polygon, is

118975 Let \(\mathbf{T}_{\mathbf{n}}\) denote the number of triangles which can be formed using the vertices of a regular polygon of \(n\) sides. If \(T_{n+1}-T_n=21\), then \(n\) equals to

118968 In how many ways 7 men and 7 women can be seated around a round table such that no two women can sit together
#[Qdiff: Hard, QCat: Numerical Based, examname: Now, [MHT CET-2021], no two women are to sit together as such the 7 women are to be arranged in seven empty seats between two consecutive men and number of arrangement will be 7 Hence, by fundamental theorem the total number ways \(=7 ! \times 6 !\), 65. A committee of 4 is to selected from 4 Engineers, 6 Doctors and 5 Lawyers. The number of ways in which there is at least one from each profession is,

118973 The number of ways in which the letters \(x_1\), \(\mathrm{x}_2, \ldots \mathrm{x}_{10,} \mathrm{y}_1, \mathrm{y}_2, \ldots \mathrm{y}_{15}\) can be arranged in a line such that the suffixes of \(x\) and those of \(y\) are in ascending order of magnitude is

118974 In a polygon no three diagonals are concurrent. If the total number of points of intersection of diagonals interior to the polygon be 70 , then the number of diagonals of the polygon, is

118975 Let \(\mathbf{T}_{\mathbf{n}}\) denote the number of triangles which can be formed using the vertices of a regular polygon of \(n\) sides. If \(T_{n+1}-T_n=21\), then \(n\) equals to

118968 In how many ways 7 men and 7 women can be seated around a round table such that no two women can sit together
#[Qdiff: Hard, QCat: Numerical Based, examname: Now, [MHT CET-2021], no two women are to sit together as such the 7 women are to be arranged in seven empty seats between two consecutive men and number of arrangement will be 7 Hence, by fundamental theorem the total number ways \(=7 ! \times 6 !\), 65. A committee of 4 is to selected from 4 Engineers, 6 Doctors and 5 Lawyers. The number of ways in which there is at least one from each profession is,

118973 The number of ways in which the letters \(x_1\), \(\mathrm{x}_2, \ldots \mathrm{x}_{10,} \mathrm{y}_1, \mathrm{y}_2, \ldots \mathrm{y}_{15}\) can be arranged in a line such that the suffixes of \(x\) and those of \(y\) are in ascending order of magnitude is

118974 In a polygon no three diagonals are concurrent. If the total number of points of intersection of diagonals interior to the polygon be 70 , then the number of diagonals of the polygon, is

118975 Let \(\mathbf{T}_{\mathbf{n}}\) denote the number of triangles which can be formed using the vertices of a regular polygon of \(n\) sides. If \(T_{n+1}-T_n=21\), then \(n\) equals to