Permutation and Combination

1. From 7 boys and 5 girls, 6 are to be selected for admission for a particular course. In how many ways can this be done if there must be exactly 3 girls?

• ক. 350
• খ. 65
• গ. 1050
• ঘ. 120

2. In a container there are 2 green marbles and 2 red marbles. You randomly pick two marbles. What is the probability that both of them are green?

• ক. 1/2
• খ. 1/3
• গ. 1/6
• ঘ. 1/8

3. 120 students in a class play cricket or football or both. If 75 students play cricket and 60 students play football, how many play both?

• ক. 15
• খ. 16
• গ. 76
• ঘ. 38

4. From 6 boys and 4 girls, 5 are to be selected for admission for a particular course. In how many ways can this be done if there must be exactly 2 girls?

• ক. 60
• খ. 30
• গ. 90
• ঘ. 120

5. In Rajshahi 5 adults are unemployed for every 120 who have jobs. Out of 2125 adults how many have jobs?

• ক. 2040
• খ. 1896
• গ. 425
• ঘ. 89

6. There are 20 members in a football squad. In electing a captain and a vice-captain, how many different outcomes of the election possible?

• ক. 20
• খ. 39
• গ. 190
• ঘ. 380

7. The area of a rectangle R with width 4 feet is equal to the area of a square S which has a perimeter of 24 feet. The perimeter of the rectangle R in feet is--

• ক. 9
• খ. 16
• গ. 24
• ঘ. 26

8. How many signals can be given by 5 flags of different colours using 3 flags at a time.

• ক. 5
• খ. 15
• গ. 60
• ঘ. 120

9. How many combinations are possible if a person has 4 sports jackets, 5 shirts and 3 pair of socks?

• ক. 4
• খ. 5
• গ. 60
• ঘ. 12

10. Rahima wanted to arrange 3 of her 4 plants in a row on a shelf. If each of the plants is in a different colored container, how many different arrangements can she make?

• ক. 24
• খ. 28
• গ. 36
• ঘ. 7

11. How many different committees of 3 members can be chosen out of 5 persons in a group so that one particular person is always chosen?

• ক. 6
• খ. 8
• গ. 4
• ঘ. 5

12. A club has 8 male & 8 female members. The club is choosing a committee of 6 members. The committee must have 3 male & 3 female members. How many different committees can be chosen?

• ক. 720
• খ. 112
• গ. 9
• ঘ. 3136

13. When a meeting of a committee was over every member shook hands with one another & the total number of handshske was 6. How many members were there in the meeting?

• ক. 4
• খ. 5
• গ. 6
• ঘ. 2

14. 36 identical chairs must be arranged in rows with equal number of chairs in each row. Each row must be contain at least 3 chairs & there must be at least 3 rows. How many different arrangements are possible?

• ক. 2
• খ. 4
• গ. 5
• ঘ. 6

15. Form a group of 7 men & 6 women 5 persons are to be selected to from acommittee so that at least 3 men are there on the committee. In how many ways can it be done?

• ক. 564
• খ. 645
• গ. 800
• ঘ. 756

16. In how many ways can a subcommittee of five persons be formed from amongst 4 women & 6 men so that one particular man and one particular woman is always included?

• ক. 56
• খ. 58
• গ. 64
• ঘ. 30

17. When a meeting of a committee was over every member shook hands with one another & the total number of handshakes was 10. How many members were there meeting?

• ক. 4
• খ. 5
• গ. 6
• ঘ. 2

18. In how many ways can the letters of the word 'LEADER' be arranged?

• ক. 72
• খ. 144
• গ. 360
• ঘ. 720