Question

in how many ways can 5 different books be arranged in shelf ? if there are no restrictions
1) there are no restrictions
2) 2 books are always together
3) 2 books are never together​

Answer 1

Answer:

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Answer 2

Given,

Total number of books = 5

To find,

We have to find the number of ways by which books can be arranged on the shelf if

1) there are no restrictions

2) 2 books are always together

3) 2 books are never together​

Solution,

The number of ways by which books can be arranged on the shelf is 120, 48, and 72 respectively.

We can simply find the required number of ways by which 5 different books can be arranged by the concepts of Permutations,

(1) There are 5 different books that can be arranged in 5! ways.

         The total number of ways = 5!

                                                       = 120

(2) The two books are always together. The two books can arrange themselves in 2! ways,

The remaining books can arrange themselves in 4! ways,

So, the total number of arrangements = 2! * 4!

                                                                  = 48

(3) The two books are never together, so the total number of ways can be found out by subtracting the number of cases when 2 books are always together from the total number of ways of arranging the 5 different books.

The total number of ways = 120-48

                                             = 72

Hence, the required number of different ways of arranging 5 different books are 120, 48, and 72 respectively.