6 people consisting of 3 couples are seated in a row of 6 chairs to take group pictures. (a) In how many ways could they be seated? (b)How many ways could they be seated if each couple should sit next to each other? Justify your answer. (c) One of the couples broke up and do not want to sit next to each other. Whereas the other 4 want to sit next to their partners. In how many ways could they be seated?
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.
6 people consisting of 3 couples are seated in a row of 6 chairs to take group pictures.
(a) In how many ways could they be seated?
(b)How many ways could they be seated if each couple should sit next to each other?
Justify your answer.
(c) One of the couples broke up and do not want to sit next to each other. Whereas the other 4 want to sit next to their partners. In how many ways could they be seated?
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