A baseball manager has 12 players on his team but only nine players can play on the field at one time. (a) How many different trios of players can the manager leave on the bench (that is to say not playing in the field)? (b) How many different starting lineups (where batting order is important) of 9 players can the manager create?
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.
A baseball manager has 12 players on his team but only nine players can play on the field at one time.
(a) How many different trios of players can the manager leave on the bench (that is to say not playing in the field)?
(b) How many different starting lineups (where batting order is important) of 9 players can the manager create?
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