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Combinations and Permutations Exam #1

1. How many different committees of 4 members can be formed from a group with 7 seniors and 6 juniors?

715

 

2. How many different committees with 4 members can be formed from a group with 7 seniors and 6 juniors if they are all seniors? *
1 point
35

3. How many different committees with 4 members can be formed from a group with 7 seniors and 6 juniors if there are 3 seniors and 1 junior?
210

4. How many different committees with 4 members can be formed from a group with 7 seniors and 6 juniors if there are equal number of seniors and juniors in each committee?
315

Source: LINK

5. A class consists of 12 boys and 10 girls. In how many ways can a committee of five be formed if all the members are boys?
792

 

6. A class consists of 12 boys and 10 girls. In how many ways can a committee of five be formed if 2 are boys and 3 are girls?
7920

Source: LINK

 

7. A box contains 2 red, 5 blue and 5 yellow balls. In how many can 3 balls be drawn?

220

 

8.  A box contains 2 red, 5 blue and 5 yellow balls. In how many ways can three balls be drawn from the box such that they are all blue?

10

 

9. A box contains 2 red, 5 blue and 5 yellow balls. In how many ways can three balls be drawn from the box such that there are no blue balls?35

10. A box contains 2 red, 5 blue and 5 yellow balls. In how many ways can three balls be drawn from the box such that 2 are red and 1 is yellow?
5

 

11. A box contains 2 red, 5 blue and 5 yellow balls. In how many ways can three balls be drawn from the box such that they are of different colors?
50

Source: LINK

12. In how many ways can a student answer an exam if out of the 6 problems he is required to answer only 5?

6

Source: LINK

 

13. In a given examination a student is required to answer 5 out of the 7 questions including 3 of the first 4 questions. In how many can he answer the examination?

12

Source: LINK

 

14. A box contains 3 black and 5 red balls. In how many ways can 2 balls be drawn from the box such that 1 is black and 1 is red?

15

 

15. A lot contains 20 electric bulbs 5 of which are defective. In how many ways can 4 bulbs be taken for inspection such that no defective electric bulb is included?
1365

16. A lot contains 20 electric bulbs 5 of which are defective. In how many ways can 4 bulbs be taken for inspection such that 2 of the defective bulbs are included?
1050

17. A lot contains 20 electric bulbs 5 of which are defective. In how many ways can 4 bulbs be taken for inspection such that all of the defective bulbs are included?

5

 

18. A shipment of 10 TV sets contains 2 units that are defective. In how many ways can 3 TV sets be inspected such that no defective TV set is included?
56

19. A shipment of 10 TV sets contains 2 units that are defective. In how many ways can 3 TV sets be inspected such that both defective TV sets are included for inspection?
8

20. A shipment of 10 TV sets contains 2 units that are defective. In how many ways can 3 TV sets be inspected such that only one of the defective TV sets is included?
56

For numbers 21-30. Evaluate each expression.
21. (3C2)
3

22. (7C2)
21

23. (6C4)
15

24. (12C9)
220

25. (5C2)
10

26. (6C2 + 6C3 + 6C4)
50

27. (4C0 + 4C1 + 4C2 + 4C3 + 4C4)
16

28. (7C3 + 7C4 + 7C5 + 7C6 + 7C7)
99

29. 2(5P3 – 6C2)
90

30. 5(5C3 x 6C3)
1000

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