The number of ways is 18C5 = 18!/(5!*13!) = 8,568 ways.
-5
4
3 people can be selected from a pool of 7 people in (7 x 6 x 5) = 210 ways.But each group of 3 can be selected and seated in (3 x 2 x 1) = 6 ways.So the number of different 3-person subcommittees formed from 7 people is (210/6) = 35 .
Four people can be selected from a pool of 8 people in (8 x 7 x 6 x 5) = 1,680 ways.But there are (4 x 3 x 2) = 24 ways to pick the same four people.So you can actually form only 1,680/24 = 70 different 4-person debate teamsfrom a group of 8 students.
-6
5 for 2, 3 for 3, 2 for 4.
-5
Nine people can be selected from the group in(12 x 11 x 10 x 9 x 8 x 7 x 6 x 5 x 4) = 79,833,600ways.But each group of the same 9 people can be selected in(9 x 8 x 7 x 6 x 5 x 4 x 3 x 2) = 362,880 different orders.So the number of different 9-person committees that can be selected is79,833,600/362,880 = 220 .
Nine people can be selected from the group of 12 in(12 x 11 x 10 x 9 x 8 x 7 x 6 x 5 x 4) = 79,833,600ways.But each group of the same 9 people can be selected in(9 x 8 x 7 x 6 x 5 x 4 x 3 x 2) = 362,880 different orders.So the number of different 9-person committees that can be selected is79,833,600/362,880 = 220 .
-5
4
4 people can be selected from a pool of 15 people in (15 x 14 x 13 x 12) = 32,760 ways.But each group of 4 can be selected and seated in (4 x 3 x 2 x 1) = 24 ways.So the number of different 4-person subcommittees formed from 15 people is (32,760 / 4) = 8,190 .
the answer is 3 because 3 6's go into 18
One.
3 people can be selected from a pool of 7 people in (7 x 6 x 5) = 210 ways.But each group of 3 can be selected and seated in (3 x 2 x 1) = 6 ways.So the number of different 3-person subcommittees formed from 7 people is (210/6) = 35 .
35
Four people can be selected from a pool of 8 people in (8 x 7 x 6 x 5) = 1,680 ways.But there are (4 x 3 x 2) = 24 ways to pick the same four people.So you can actually form only 1,680/24 = 70 different 4-person debate teamsfrom a group of 8 students.