Five boys and five girls form a line. Find the number of ways of making the seating arrangement under the following condition.

Eighteen guests are to be seated, half on each side of a long table. Four particular guests desire to sit on one p[articular side and three others on other side of the table. The number of ways in which the seating arrangements can be made is (11!)/(5!6!)xx 9!xx 9!.

If a train, five seats are vacant, the number of ways three passengers can sit, is

Find the number of ways in which 12 different beads can be arranged to form a necklace.

Out of 18 points in a plane, no three are in the same line except five points which are collinear. Find the number of lines that can be formed joining the point.

Find the number of solutions of x + y + z + w = 20 under the following conditions: , x ge 0, y ge 0, z ge 0, w ge0

There are 10 lamps in a hall, Each one of them can be switched on independently. Find the number of ways in which the hall can be illuminted, Thinking Process : Total numbers of ways to lightned room is out of given n bulbs at least one or all bulls are lightened. we get total number of ways using following fromula.

Form the pair of linear equations in the following problems and find their solutions (if they exist) by any algebraic method: A part of monthly hostel charges is fixed and the remaining depends on the number of days one has taken food in the mess. When a student A takes food for 20 days she has to pay Rs. 1000 as hostel charges while student B takes food for 26 days, pays Rs. 1180 as hostel charges. Find the fixed charges and the cost of food per day.

There are five points A,B,C,D and E. no three points are collinear and no four are concyclic. If the line AB intersects of the circles drawn through the five points. The number of points of intersection on the line apart from A and B is

If all the words (with or without meaning) having five letters, formed using the letters of the word SMALL and arranged as in a dictionary; then the position of the word SMALL is :