Keiko has 7 colors of lanyard. She uses 3 different colors to make a keychain. How many different combinations can she choose?
7 for the first, 6 for the second and 5 for the third. The answer is the product of those numbers, no matter what order the three colors are picked. The number of possibilities in "combination" problemsa like this can written in the form
7!/(7-3)! = 7!/4! = 7x6x5
Write out the possibilities.
All of them.
Then count them.
Tada! Ur answer will appear.
:D
28
Keiko has six colors of lanyard. She uses two different
colors to make a key chain. How many different combinations
can she choose?
To find all the different combinations that Keiko can choose, we can list out all the possibilities by selecting 3 colors from the 7 colors of lanyard she has.
Here are all the possible combinations:
1. Color 1, Color 2, Color 3
2. Color 1, Color 2, Color 4
3. Color 1, Color 2, Color 5
4. Color 1, Color 2, Color 6
5. Color 1, Color 2, Color 7
6. Color 1, Color 3, Color 4
7. Color 1, Color 3, Color 5
8. Color 1, Color 3, Color 6
9. Color 1, Color 3, Color 7
10. Color 1, Color 4, Color 5
11. Color 1, Color 4, Color 6
12. Color 1, Color 4, Color 7
13. Color 1, Color 5, Color 6
14. Color 1, Color 5, Color 7
15. Color 1, Color 6, Color 7
16. Color 2, Color 3, Color 4
17. Color 2, Color 3, Color 5
18. Color 2, Color 3, Color 6
19. Color 2, Color 3, Color 7
20. Color 2, Color 4, Color 5
21. Color 2, Color 4, Color 6
22. Color 2, Color 4, Color 7
23. Color 2, Color 5, Color 6
24. Color 2, Color 5, Color 7
25. Color 2, Color 6, Color 7
26. Color 3, Color 4, Color 5
27. Color 3, Color 4, Color 6
28. Color 3, Color 4, Color 7
29. Color 3, Color 5, Color 6
30. Color 3, Color 5, Color 7
31. Color 3, Color 6, Color 7
32. Color 4, Color 5, Color 6
33. Color 4, Color 5, Color 7
34. Color 4, Color 6, Color 7
35. Color 5, Color 6, Color 7
Counting the possibilities, there are a total of 35 different combinations that Keiko can choose to make a keychain.
To find all the possible combinations, we can list them out systematically:
1. Red, Blue, Green
2. Red, Blue, Yellow
3. Red, Blue, Orange
4. Red, Blue, Violet
5. Red, Blue, Indigo
6. Red, Blue, Pink
7. Red, Green, Blue
8. Red, Green, Yellow
9. Red, Green, Orange
10. Red, Green, Violet
11. Red, Green, Indigo
12. Red, Green, Pink
13. Red, Yellow, Blue
14. Red, Yellow, Green
15. Red, Yellow, Orange
16. Red, Yellow, Violet
17. Red, Yellow, Indigo
18. Red, Yellow, Pink
19. Red, Orange, Blue
20. Red, Orange, Green
21. Red, Orange, Yellow
22. Red, Orange, Violet
23. Red, Orange, Indigo
24. Red, Orange, Pink
25. Red, Violet, Blue
26. Red, Violet, Green
27. Red, Violet, Yellow
28. Red, Violet, Orange
29. Red, Violet, Indigo
30. Red, Violet, Pink
31. Red, Indigo, Blue
32. Red, Indigo, Green
33. Red, Indigo, Yellow
34. Red, Indigo, Orange
35. Red, Indigo, Violet
36. Red, Indigo, Pink
37. Red, Pink, Blue
38. Red, Pink, Green
39. Red, Pink, Yellow
40. Red, Pink, Orange
41. Red, Pink, Violet
42. Red, Pink, Indigo
And so on, until we have listed out all the possibilities. Now, we can count the number of combinations. In this case, we can see that there are 42 different combinations that Keiko can choose from.