For this problem, assume 9 males audition, one of them being Roger, 4 females audition, one of them being Merna, and 5 children audition. The casting director has 4 male roles available, 2 female roles available, and 1 child role available. (1) How many different ways can these roles be filled from these auditioners? (2) How many different ways can these roles be filled if exactly one of Roger and Merna gets a part? (3) What is the probability (if the roles are filled at random) of both Roger and Merna getting a part?
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.
For this problem, assume 9 males audition, one of them being Roger, 4 females audition, one of them being Merna, and 5 children audition. The casting director has 4 male roles available, 2 female roles available, and 1 child role available.
(1) How many different ways can these roles be filled from these auditioners?
(2) How many different ways can these roles be filled if exactly one of Roger and Merna gets a part?
(3) What is the probability (if the roles are filled at random) of both Roger and Merna getting a part?
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