A quality control inspector samples 4 computer chips from a box containing 12 computer chips. If the box contains 2 defective chips, in how many ways can he select a sample so that both defective chips are selected?
There are 2 defective chips and 10 good chips.
1. We choose the defective ones:
That's "2 choose 2" = 2C2 = (2*1)/(2*1) = 1 way
2. We choose the 2 good chips:
That's "10 choose 2" = 10C2 = (10*9)/(2*1) = 45 ways
That's 2C2*10C2 = 1*45 = 45 ways.
Checking:
Suppose the chips are A,B,C,D,E,F,G,H,I,J,X,Y
where A through J are the 10 good chips and X and Y are the 2 defective ones.
Here are the 45 ways he can select 4 including the 2 defective chips
X and Y:
1. {X,Y,A,B}
2. {X,Y,A,C}
3. {X,Y,A,D}
4. {X,Y,A,E}
5. {X,Y,A,F}
6. {X,Y,A,G}
7. {X,Y,A,H}
8. {X,Y,A,I}
9. {X,Y,A,J}
10. {X,Y,B,C}
11. {X,Y,B,D}
12. {X,Y,B,E}
13. {X,Y,B,F}
14. {X,Y,B,G}
15. {X,Y,B,H}
16. {X,Y,B,I}
17. {X,Y,B,J}
18. {X,Y,C,D}
19. {X,Y,C,E}
20. {X,Y,C,F}
21. {X,Y,C,G}
22. {X,Y,C,H}
23. {X,Y,C,I}
24. {X,Y,C,J}
25. {X,Y,D,E}
26. {X,Y,D,F}
27. {X,Y,D,G}
28. {X,Y,D,H}
29. {X,Y,D,I}
30. {X,Y,D,J}
31. {X,Y,E,F}
32. {X,Y,E,G}
33. {X,Y,E,H}
34. {X,Y,E,I}
35. {X,Y,E,J}
36. {X,Y,F,G}
37. {X,Y,F,H}
38. {X,Y,F,I}
39. {X,Y,F,J}
40. {X,Y,G,H}
41. {X,Y,G,I}
42. {X,Y,G,J}
43. {X,Y,H,I}
44. {X,Y,H,J}
45. {X,Y,I,J}
Edwin
