SCUBA club consists of 9 divers with advanced certification and 6 with just a basic certification. They are planning a dive for 4 of their members. a) How many ways can these four members be chosen if there are no restrictions? b) If the club rules state that at least one of these 4 members must have advanced certification then how many ways can the selection be made if just one selected member has advanced certification?
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 SCUBA club consists of 9 divers with advanced certification and 6 with just a basic certification. They are planning a dive for 4 of their members.
a) How many ways can these four members be chosen if there are no restrictions?
b) If the club rules state that at least one of these 4 members must have advanced certification then how many ways can the selection be made if just one selected member has advanced certification?
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