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.
The number of ways is 18C5 = 18!/(5!*13!) = 8,568 ways.
There are 8!/(4!*4!) = 70 ways.
Infinitely many.
If order matters, 50x49x48x47 = 5,527,200. If the order doesn't matter (which it probably doesn't, given that we're not selecting the winner, first runner-up, etc. directly), it's slightly trickier: there are 4!, or 24, ways of arranging four items, so we have to divide the larger number by 24 to get 230,300.
In how many ways can fourfour women be selected from the eighteight ​women
-1
24 ways to make this selection.
They can be selected in 756 ways.
If there are 58 defective circuit boards, two can be selected in 58*57/2 = 1653 ways.
18x17= 306 ways
53,130 ways.
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.
35
30240
Four Ways to Forgiveness has 228 pages.
19 Republicans choose 3 and 12 Democrats choose 2. This is written as 19C3 * 12C2; or 969*66 or 63954 ways can a subcommittee be assembled if it must contain 3 Republicans and 2 Democrats as stated in the question.