Arne, Bobbette, Chuck, Deirdre, Ed, and Fran have reserved six seats in a row at the theater, starting at an aisle seat. In how many ways can they arrange themselves? (Hint: Divide the task into the series of six parts shown below, performed in that order.) (a) If A is seated first, how many seats are available for him? (b) Now, how many are available for B? (c) Now, how many for C? (d) Now, how many for D? (e) Now, how many for E? (f) Now, how many for F? Now multiply your six answers above.
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.
Trending now
This is a popular solution!
Step by step
Solved in 2 steps with 2 images
