The English alphabet has 5 vowels and 21 consonants. How many words with two different vowels and 2 different consonants can be formed from the alphabet?

In an examination, a paper consists of 12 Qs divided into 2 parts i.e., Part I and Part II, containing 5 and 7 Qs, respectively. A student is required to attempt 8 Qs in all, selecting at least 3 from each part. In how many ways can a student select the Qs?

Determine the number of 5-card combinations out of a deck of 52 cards if each selection of 5 cards has exactly one king.

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.