Five applicants (Jim, Don, Mary, Sue, and Nancy) are available for two identical jobs. A supervisor selects two applicants to fill these jobs. a. List all possible ways in which the jobs can be filled. (That is, list all possible selections of two applicants from the five.) b. Let A denote the set of selections containing at least one male. How many elements are in A? c. Let B denote the set of selections containing exactly one male, How many elements are in B?
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.
Five applicants (Jim, Don, Mary, Sue, and Nancy) are available for two identical jobs. A supervisor selects two applicants to fill these jobs.
a. List all possible ways in which the jobs can be filled. (That is, list all possible selections of two applicants from the five.)
b. Let A denote the set of selections containing at least one male. How many elements are in A?
c. Let B denote the set of selections containing exactly one male, How many elements are in B?
d. Write the set containing two females in terms of A and B.
e. List the elements in !A, AB, AuB (union), and !(AB).
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