(b) A young boy asked his mother to get 6 game cartridges from his selection of 11 arcade and 7 sport games. How many ways are there that his mother will get 4 arcade and 2 sports games? (c) In a cricket team there are 12 players, among these 12 players there is one captain, 4 batsmen, 3 all-rounders, 3 regular bowlers and one extra player. How many different ways can they be arranged?
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.
(b) A young boy asked his mother to get 6 game cartridges from his selection of 11 arcade and 7 sport games. How many ways are there that his mother will get 4 arcade and 2 sports games?
(c) In a cricket team there are 12 players, among these 12 players there is one captain, 4 batsmen, 3 all-rounders, 3 regular bowlers and one extra player. How many different ways can they be arranged?
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