In how many ways can 8 Indians and, 4 American and 4 Englishmen can be seated in a row so that all person of the same nationality sit together?

How many Permutations of the letters of the word APPLE are there?

How many different words can be formed using all the letters of the word ALLAHABAD?
(a) When vowels occupy the even positions.
(b) Both L do not occur together.

In how many ways can 10 examination papers be arranged so that the best and the worst papers never come together?

In how many ways 4 boys and 3 girls can be seated in a row so that they are alternate.

A two member committee comprising of one male and one female member is to be constitute out of five males and three females. Amongst the females. Ms. A refuses to be a member of the committee in which Mr. B is taken as the member. In how many different ways can the committee be constituted ?

In how many ways 2 students can be chosen from the class of 20 students?

Three gentlemen and three ladies are candidates for two vacancies. A voter has to vote for two candidates. In how many ways can one cast his vote?

A question paper has two parts, A and B, each containing 10 questions. If a student has to choose 8 from part A and 5 from part B, in how many ways can he choose the questions?

Find the number of triangles which can be formed by joining the angular points of a polygon of 8 sides as vertices.

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