Of the 25 people in the school’s BETA club, 5 serve on the leadership committee. How many ways are there to select members for this committee? Show your work in the space provided. 5.) 5 Letters are to be picked for the word APPLICATIONS. How many selections contain at least one A? Show your work in the space provided. 6.) In a production of West Side Story, eight actors are considered for the male roles of Tony, Riff, and Bernardo. How many ways can the director cast the male roles? Show your work in the space provided.
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.
Solve each of the following application problems. You need to use the online permutation and combination calculators to solve application problems #4, #5, and #6. Links to the online calculators are provided on the Task page.
1.) Calculate the number of different ways the letters in the word SUNDAY can be arranged if all of the vowels are next to each other.
Show your work in the space provided.
2.) Calculate the number of different ways the letters in the word SATURDAY can be arranged where no two vowels are next to each other.
Show your work in the space provided.
3.) A group of 12 people consisting of 6 married couples are to be arranged in a line for a photo. How many different arrangements are there where each person is standing next to their spouse?
Show your work in the space provided.
4.) Of the 25 people in the school’s BETA club, 5 serve on the leadership committee. How many ways are there to select members for this committee?
Show your work in the space provided.
5.) 5 Letters are to be picked for the word APPLICATIONS. How many selections contain at least one A?
Show your work in the space provided.
6.) In a production of West Side Story, eight actors are considered for the male roles of Tony, Riff, and Bernardo. How many ways can the director cast the male roles?
Show your work in the space provided.
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