Mr. Jones has 10 books that he is going to put on his bookshelf. Of these, 4 are Math books, 3 are Chemistry books, 2 are History books, and 1 is a book of Counting Crows song lyrics. If Mr. Jones wants to arrange the books in such a way that all books dealing with the same subject are together, how many different arrangements are possible? (Assume the books in each category are all different.
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.
Mr. Jones has 10 books that he is going to put on his bookshelf. Of these, 4 are Math books, 3 are Chemistry
books, 2 are History books, and 1 is a book of Counting Crows song lyrics. If Mr. Jones wants to arrange the
books in such a way that all books dealing with the same subject are together, how many different
arrangements are possible? (Assume the books in each category are all different.)
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