Sam bought 9 tickets all in the same row to a KC Royals game for himself and his friends next week. His friends are Eric, Sarah, Renee, David, Julie, Derek, Kelsey and kyle. (a) How many different ways can the friends be seated in the row? (b) Sam has a crush on Sarah, so he wants to make sure his seat is next to hers. How many ways are there to assign the seats now? (c) How many ways are there to assign the seats if Sam wants to ensure that they are all seated boy-girl-boy-girl?
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.
Sam bought 9 tickets all in the same row to a KC Royals game for himself and his friends next week. His friends are Eric, Sarah, Renee, David, Julie, Derek, Kelsey and kyle.
(a) How many different ways can the friends be seated in the row?
(b) Sam has a crush on Sarah, so he wants to make sure his seat is next to hers. How many ways are there to assign the seats now?
(c) How many ways are there to assign the seats if Sam wants to ensure that they are all seated boy-girl-boy-girl?
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