In how many ways can the coach choose 11 players to play? |A lineup describes the set of players which play together. A lineup consists of: 4 midfielders, 3 defenders, 3 attackers and 1 goalkeeper. This team has: 7 midfielders, 6 defenders, 5 attackers and 2 goalkeepers in total on their roster. In how many ways can the coach choose a lineup of players? Now assume that one of the defenders, after a summer or practice, may play the attack position in addition to defense. In how many ways can the coach choose a lineup?
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.
Trending now
This is a popular solution!
Step by step
Solved in 2 steps
