1. 8 members of a matching band are auditioning for 3 lead positions. In how many ways can students be chosen for the lead positions? ( Please explain how you know if this is combination or permutation )
2. Year has an editor and assistant editor positions. The staff of the yearbook is 15. In how many ways can students be chosen for these two positions?( Please explain how you know if this is combination or permutation )
3. A relay race has 4 runners who run different parts of race. There are 16 students on your track team. In how many ways can your coach select students to compete in the race? ( Please explain how you know if this is combination or permutation )
4. You must take 6 elective classes to graduate. There are 12 classes that you are interested in. How many ways can you select your electives? ( Please explain how you know if this is combination or permutation )
2. Year has an editor and assistant editor positions. The staff of the yearbook is 15. In how many ways can students be chosen for these two positions?( Please explain how you know if this is combination or permutation )
3. A relay race has 4 runners who run different parts of race. There are 16 students on your track team. In how many ways can your coach select students to compete in the race? ( Please explain how you know if this is combination or permutation )
4. You must take 6 elective classes to graduate. There are 12 classes that you are interested in. How many ways can you select your electives? ( Please explain how you know if this is combination or permutation )
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In general, permutation: order matters, combination: does not matter.
1) Combination. Say you want to choose A, B, and C for the lead positions. Order doesn't matter, i.e. you could select B, C, and A & still have the same thing.
2) Independent Combination. Namely, 15 choices for the editor, and 14c2 for assistant editor.
3) I believe this should be a permutation, because it matters which students go first.
4) Combination, doesn't matter which order you take the class(unless there are prereqs and stuff)
1) Combination. Say you want to choose A, B, and C for the lead positions. Order doesn't matter, i.e. you could select B, C, and A & still have the same thing.
2) Independent Combination. Namely, 15 choices for the editor, and 14c2 for assistant editor.
3) I believe this should be a permutation, because it matters which students go first.
4) Combination, doesn't matter which order you take the class(unless there are prereqs and stuff)