There are 4 books on fairy tales, 5 novels and 3 plays. a) In how many ways can you arrange these so that books on fairy tales are together, novels are together and plays are together and in the order, books on fairytales, novels and plays b) In how many ways can you arrange these so that books on fairy tales are together, novels are together, and plays are together, but we no longer require that they should be in specific order?
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.
There are 4 books on fairy tales, 5 novels and 3 plays.
a) In how many ways can you arrange these so that books on fairy tales are together, novels are together and plays are together and in the order, books on fairytales, novels and plays
b) In how many ways can you arrange these so that books on fairy tales are together, novels are together, and plays are together, but we no longer require that they should be in specific order?
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