## 1. 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?

## 2. How many Permutations of the letters of the word APPLE are there?

## 3. 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.

(a) When vowels occupy the even positions.

(b) Both L do not occur together.

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

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

## 6. 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 ?

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

## 8. 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?

## 9. 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?

## 10. 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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