It is required to seat 5 men and 4 women in a row so that the women can occupy the even places. 

How many such arrangements are possible?

From the class of 25 students, 10 are to be chosen for an excursion party. There are 3 students who decide that either all of them will join or none of them will join. In how many ways can the excursion party be chosen?

In how many words can the letters of the word ASSASSINATION be arranged so that all the S’s are together?

1 and 2 deals with the formation of 3-digit numbers using the multiplication rule when repetition is allowed, and when not allowed

Show that the three forces directed from the vertices and represented by the three median of a tringle , are in equalibrium.

ABC is a tringle and D ,E,F are the middle points of the sides . Forces represented by AD, 2/3 BE and 1/3 CF act on a particle at the point where AD and BE meet.Show that the resultant is represunted in magnitude and direction by 1/2 AC and that its line of action divided in the ratio 2:1.

Find a point O within a tringle ABC so that the forces represented by OA ,OB and OC in magnitude and direction and acting at O,may be in equalibrium.

If G is the centriod of tringle ABC, Show that : 

1) Forces acting on a particle and represented  by GA, GB, GC are in equalibrium .

2) Forces is represented by GD,GE, GF are in equalibrium , where D,E, F are mid points of BC,AC and AB repectively.

P is any point on tringle ABC and D,E,F are the mid point of the sides . prove that forces represented by AP, BP, CP, PD, PE, PF are in equalibium.

If P is the point in any plane of the tringle ABC  show that the forces PA, PB, PC are equal to 3PG, where G is the centriod of the tringle.

ABCD is a quadrilateral. Forces is represent by BC, BA, DC, DA are acting at a point . show that the resultant will be represented by four times the line joining the mid points of the diagonal.