Quantitative Reasoning Permutation and Combination Test 2

1. Two series of a question-booklet for an aptitude test are to be given to twelve students. In how many ways can the students be placed in two rows of six each so that there should be no identical series side by side and that the students sitting one behind the other should have the same series?

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2. In a class-room, there are 6 students. We need to divide them into 3 pairs for the purpose of assigning homework. In how many ways can we make such pairs?

3. A cricket team of 11 players is to be formed from 20 players including 6 bowlers and 3 wicket keepers. The number of ways in which a team can be formed having exactly 4 bowlers and 2 wicketkeeper is?

4. The letters of the word PROMISE are arranged so that no two of the vowels should come together. Find the total number of arrangements.

5. Out of eight crew members three particular members can sit only on the left side. Another two particular members can sit only on the right side. Find the number of ways in which the crew can be arranged so that four men can sit on each side.

6. There boys and three girls are to be seated around a table in a circle. Among them the boy X does not want any girl neighbor and the girl Y does not want any boy neighbor. How many such arrangements are possible?

7. When a group photograph is taken, all the seven teachers should be in the first row and all the twenty students should be in the second row. If the two corners of the second row are reserved for the two tallest students, interchangeable only between them, and if the middle seat of the front row is reserved for the principal; the number of such possible 'arrangements' is?

8. A class photograph has to be taken. The front now consists of 6 girls who are sitting. 20 boys are standing behind. The two corner positions are reserved for the two tallest boys. In how many ways can the students be arranged?

9. A box contains 10 balls out of which 3 are red and the rest are blue. In how many ways can a random sample of 6 balls be drawn from the bag so that at the most 2 red balls are included in the sample and no sample has all the 6 balls of the same color?

10. The number of ways in which a team of eleven players can be selected from 22 players including 2 of them and excluding 4 of them is?

11. In a certain city, all telephone numbers have six digits, the first two digits always being 41 or 42 or 46 or 62 or 64. The number of telephone numbers having all six digits distinct is?