How many different 4-person teams (order does not matter) can be put together from a group of 27 people? A) There are 27 x 26 x 25 x 24 different possible teams, because for each spot on the team, you choose from the number of people available in the group, which decreases by 1 after each selection, and order does not matter. B) There are 27 x 26 x 25 x 24 different possible teams, because for each spot on the team, you choose from the number of people available in the group, which decreases by 1 after each selection, and order matters. C) There are 27×26×25×244×3×2×1, different possible teams, because all players come from one group, nobody is selected twice, and the order does not matter. D) There are 27! different possible teams, because for each spot on the team, there is one fewer person from the group to choose from. E) There are 27×26×25×244×3×2×1, different possible teams, because all players come from one group, nobody is selected twice, and order matters.
Permutations and Combinations
If there are 5 dishes, they can be relished in any order at a time. In permutation, it should be in a particular order. In combination, the order does not matter. Take 3 letters a, b, and c. The possible ways of pairing any two letters are ab, bc, ac, ba, cb and ca. It is in a particular order. So, this can be called the permutation of a, b, and c. But if the order does not matter then ab is the same as ba. Similarly, bc is the same as cb and ac is the same as ca. Here the list has ab, bc, and ac alone. This can be called the combination of a, b, and c.
Counting Theory
The fundamental counting principle is a rule that is used to count the total number of possible outcomes in a given situation.
How many different 4-person teams (order does not matter) can be put together from a group of 27 people?
A) There are 27 x 26 x 25 x 24 different possible teams, because for each spot on the team, you choose from the number of people available in the group, which decreases by 1 after each selection, and order does not matter.
B) There are 27 x 26 x 25 x 24 different possible teams, because for each spot on the team, you choose from the number of people available in the group, which decreases by 1 after each selection, and order matters.
C) There are 27×26×25×244×3×2×1, different possible teams, because all players come from one group, nobody is selected twice, and the order does not matter.
E) There are 27×26×25×244×3×2×1, different possible teams, because all players come from one group, nobody is selected twice, and order matters.
Trending now
This is a popular solution!
Step by step
Solved in 3 steps with 2 images
