1. The manager of the Yankees has to choose 28 players for an upcoming game agai the Phillies. On his 40-man roster, he has 23 pitchers, 2 catchers, 6 outfielders, an infielders. (a) How many 28 player teams can he form if he needs 15 pitchers, 2 catchers, 5 outfielders, and 6 infielders? (b) The manager now needs to create a batting order of 9 players for the game. Th are 15 pitchers, 2 catchers, and 11 position players. How many different batt orders can be formed if the first seven must be position players, a catcher must eighth, and the pitcher be last?
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.
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